"Gödel, Escher, Bach" goes into a detailed discussion about this.
On top of that, GP is talking about hardware that builds its own copies, possibly imperfect copies. That implies a lot of information relevant to the organism may not be directly visible in the DNA - it may sit within the replication machinery, and evolve there. It's kind of similar to the difference between machine code and microcode + actual traces in silicon.
A famous Turing Award Lecture by Ken Thompson, "Reflections on Trusting Trust", provides another example[0]. Consider a C compiler. How do you build one? From its C source code, using a different C compiler. Now imagine a malicious C compiler that a) injects a trojan into the compiled binary whenever it compiles, say, "login" program, and b) injects a trojan into the binary whenever it compiles another C compiler; that second trojan contains the code for injecting a) and b). You use that compiler to recompile the original C compiler, install it in a system - and from now on, not only "login" will be bugged, but you can't get a non-malicious compiler by recompiling the original one from source; the source contains no traces of the trojans, but they are there, in the binary of the compiler you're using, and they self-replicate.
This is what I believe happens with life.
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[0] - https://www.cs.cmu.edu/~rdriley/487/papers/Thompson_1984_Ref...
GGP here. This ^, and yes, not epigenetics.
DNA is the code. Epigenetics are config options which can be saved to a file and passed on. The cell is the machine which interprets the DNA + config options.
So there are three pieces, and I don't think OP was talking about epigenetics.
To make an analogy to software, a common pattern is to have a monolithic repo with many different "personalities" (codepaths / configurations) that utilize different subsets of the monolith. DNA seems to work under a similar principle, a given cell will preferentially transcribe parts of the DNA based on epigenetic factors.
https://www.thieme-connect.de/products/ejournals/abstract/10...