Is a misconception that DNA is enough by itself to replicate a living being, there are biological bases in the embryon that need to be pass down from the parent as biological infraestructure for the new being to form.
You're absolutely correct, just as you'd be correct to observe that these 256 bytes require a fairly complex software platform running on fairly complex hardware.
And all these things, including us, operate within the fabric of the universe, whose complexity is only beginning to be understood.
But in theory, would it be possible to genetically engineer a simple life form, like a bacteria, to eventually produce a human, in a process similar to the kind of metamorphosis you see in insects. Of course, this the bootstrapping code would take quite some space, but if we could do that (at least in theory), it essentially means that all you need to make practically any living being is a single generic cell and a few megabytes worth of data encoded as DNA.
I mean, when we get infected by a virus, our cells are able to produce a completely different life form (if you consider viruses life forms), so why not going from a bacteria (which can also be infected by viruses) to a mammal. It will obviously take a lot more code, and evolution can't get us there, but the idea is similar.