I don't know what your contentions are with Snyder's Batman, but I have issues with cinematic Batmen killing. But, literally EVERY one of them HAS killed except Clooney.
So, as such, as much as I will maintain such change is NOT necessary, and IS a DEEP contradiction of the character, I also recognize the idiocy of ONLY holding Snyder's feet to the fire over it. In fact, I also recognize that it bothers me MORE with Snyder's BECAUSE in nearly every other way he is the CLOSEST we've ever seen to his paperback counterpart.
What makes Snyder's approach to Batman killing work for me, and in a way that's superior to those other takes, is that his film understands that the killing is problematic. In that way, I don't feel I am being lied to or tricked as an audience member, and I also feel like Snyder and I are on the same page about what Batman should be or always be striving to be despite stumbles along the way.
Except that is purely symbolic at that point, as the Codex became useless after the Ship was destroyed. So, having the Codex in his DNA is no more significant than simply having Kryptonian DNA. Both provide just as much connection to his heritage. Actually, his Kryptonian DNA is MORE of a connection as it actually affects him.
Given Snyder's flair for the symbolic, I suspect that you're right that ultimately his take on the kill and how it relates to Krypton's survival rests heavily on its symbolism. If you track Clark's feelings about his home world, he starts as a teen being first unaware and then anxious about it. As a young adult, he becomes more interested in it, seeking information about it out and showing joy both with Jor-El's hologram and with his mother when he finally learns the truth. Zod's introduction complicates things, especially since Jor-El has explained to him Zod's crimes on Krypton and his role in his death. During Clark's contemplative conversation with Father Leone in the church, he confesses that he isn't sure if he can trust Zod or humanity. He takes a chance on both by turning himself in. What happens on the ship changes everything. In fact, when Clark is back on Earth and speaks to Martha following Zod's attack, they speak about Zod's plans. Clark says to Martha, "Mom, Zod said this Codex he's looking for can bring my people back." Martha asks, "Isn't that a good thing?" to which Clark responds, "I don't think they're interested in sharing this world."
The subsequent confrontation between Jor-El's hologram and Zod adds a further layer to this aspect of the story.
Jor-El: Our people can co-exist.
Zod: So we can suffer through years of pain trying to adapt like your son has?
Jor-El: You're talking about genocide.
Zod: Yes. And I'm arguing its merits with a ghost.
Jor-El: We're both ghosts, Zod. Can't you see that? The Krypton you're clinging onto is gone.
Krypton is itself symbolic. It represents a corrupted past, and part of what led to its destruction was the refusal of the council to act. Jor-El's interest in the survival of Krypton is centered on a fresh start. He and Lara conceive Kal in defiance of Krypton's policies, and Jor-El steals the Codex in order to facilitate this new beginning free from the corruption of what Krypton had become. While Jor-El wants to reintroduce free will, Zod wants to double down on the eugenics. As Jor-El says, "This is a second chance for all of Krypton, not just the bloodlines you deem worthy." Despite their disagreement, Zod and Jor-El both are aligned in rejecting the dithering of the council, their "endless debates" instead of action. Zod's last words before he goes to the Phantom Zone are a rebuke of Krypton's leaders, "You won't kill us yourself! You wouldn't sully your hands! But you'll damn us to a black hole for eternity! Jor-El was right. You're a pack of fools, every last one of you."
Returning to the issue of killing, the moment that is about ending the "old" Krypton the most takes place on the ship prior to Zod's death. Zod screams, "If you destroy this ship, you destroy Krypton!" to which Superman replies, "Krypton had its chance!" He doesn't say this with sadness and never reacts with sadness about it even later, and part of the reason for that is that the Krypton it represented was one that would use genesis chambers to birth only worthy bloodlines and would require the deaths of the humans Zod deems unworthy. When Superman enacted the destruction of the empty genesis chambers and the plan to use his baby ship to create the singularity that would send the Kryptonians away, he hoped Zod would go with them into a less fatal future. Zod didn't remain later because Superman had spared him the fate of the rest of his soldiers; he was fine with his links to Krypton, including Zod, being eliminated with the singularity plan.
So, when Superman ultimately has to kill Zod, it not only has echoes of the issues Zod and Jor-El had with the council, but it also represents the final death of old Krypton that Zod symbolized. He was suicidal and corrupted, just like Krypton had been, and Superman could have dithered about making a decision or have refused to sully his own hands out of fear of taking action, thus metatextually and metaphorically being beholden to a code (the no kill code) just as the Kryptonian council members' incompetence and bureaucratic impotence were a product of their imposed genetic code, but he doesn't. In choosing to act, he replicates Jor-El's own actions on Krypton. I think that's part of why Superman's so upset after the act. Having that kind of responsibility over life and death when whole worlds or cultures are at stake is a heavy burden to bear.
I also think what Snyder means by this moment informing or inspiring the no kill code in Superman has more to do with the mythology of Superman and the larger stakes of his heroic mission. With Batman, people trace his aversion to guns and killing to his parents' 'murder. With Superman, people had no such thing. I think the situation made Superman realize that he is capable of killing when there are no other options and innocent lives are at stake, and so the way it inspires his no-kill code is not only to make him more conscious of and more dedicated to proactive measures to prevent such no-win scenarios, but also to make him appreciate just how high the stakes have to be for him to justify it.
I am happy that we got many scenes of Clark with his Mom, thanks to Snyder, starting from MoS, BvS to JL, no other Superman movie was able to film as many scenes with them.
It's one of my favorite things about these movies. The only thing that would make me happier is more of Lara.
That sounds asinine now, but I can't deny how the film made me feel when I was watching it lol. I just pushed aside all the production troubles and worries and my mouth was agape from the moment the Batman/Parademon scene happened. I really enjoyed the movie and there definitely many geek-out moments. The "Superman-Flash" moment, for example. And the shirt rip. I loved it tbh. (aside from Elfman's ****** ass score) 
