Yes, but it currently requires developmentally mature individuals to build the gametes, and the "code" is so complex you couldn't really decipher it from first principles.
It would not necessary be possible, because it's incremental instructions on how to make the hardware, but based on already existing, unspecified and very complex, hardware. So the first instruction would be something like "take the stuff you have on your left and fuse it with the stuff you have on your right", both stuff being unspecified very complex protein assumed to be present.