A literal Adam and Eve, for example. A literal Noah's Flood.
I actually had an interesting encouter with some Jehovah's Witnesses recently. They seemed nice enough, and they gave me some of their literature to peruse. You know where they instantly lost me? Evolution. Because their little booklet on origins is so full of lies and misinformation that it's impossible to take them seriously. And then I'm supposed to take anything they have to say on faith? That's not gonna happen. When people are taught things which are simply untrue, and it's bundled up with a lot of other teachings that cannot be demonstrated to be true, then sometimes something's gonna shake that bundle.
Okay, first off, even assuming that DNA is a "code" (and that we're not just imposing the concept of a code onto a natural substance), that's begging the question. By all evidence we have, DNA is a code that does not come from an intelligent agent. You can't make the claim that it isn't and then back it up by claiming that we have no codes that don't come from intelligent agents.
But the assumption that DNA is a "code" in the sense you mean it is a classic creationist trope that simply doesn't apply. If I look at the water dripping onto my windowsill right now, I could impose a code onto it, a code dependent on how the water drips and how long it is between drips. Does that mean that the dripping water is a "code" that required a designer? No. We looked at a simple natural manifestation of something and implied that it was a code. Similarly, we can look at DNA, and impose a code onto it (and I will freely admit that this is pretty easy to do), but in reality, it's just chemistry.