I mean, consider our DNA. It’s basically two chains attached, each a chain of nucleotides that pair up with the other half. Guanine–Cytosine, Adenine–Thymine, you’ve all probably seen it shown as a sequence of the letters G,T,A, and C. Really, just one strand contains the whole code, but the other exists for verification (like in error-correcting), stability, and a template during replication.
Since the whole thing is spelled out using only 4 different characters, you only need to count to 4 in binary, so just 00, 01, 10, and 11, each nucleotide could be made to take up only 2 bits, each of those numbers being designated to a certain nucleotide.
If you’re just storing the raw nucleotide data, you can basically ignore any additional information to index any location, so you can pack the nucleotide data into bytes as tightly as possible. Bytes are 8 bits, so you can fit 4 2-bit nucleotides in each byte. 3.2 billion / 4 = X GB, or 0.8GB (800MB). Slightly too big for a CD.
Now, that’s just the smallest and easiest way to store the raw code for a human, and doesn’t really account for any of the code to DO anything with the data, or any of the extra stuff that actually goes on with a cell’s molecular machinery. In fact, even just making a program that goes through and just obeys all the codons sequentially and makes whatever the code says would most likely not actually create something that resembles what happens in us, since there’s a HELL of a lot more going on with genetic machinery than just reading and manufacturing amino acids.
There’s still protein markers, gene activation/deactivation and the different ways it happens, DNA folding, gene regulation, splicing, outside factors, and countless other things which we haven’t even BEGUN to discover that all significantly affect what is actually done with the DNA. This also assumes that the source DNA was perfect and didn’t have any weird little flaws like some dumb insertion that knocks a whole gene out of commission by causing a frame shift.
You may also be interested in saving storage space, and there’s ways to compress our genetic code quite a bit that nature just doesn’t do since it hasn’t come upon it. Hell, from what we’ve seen the bulk of our genetic material is garbage that doesn’t do anything, and we’ve evolved crazy complex systems to get rid of the trash and end up with just the clean code at the end. Weird phenomena in our DNA such as long stretches of a small repeating sequence (from what I hear the Y chromosome in humans is mostly this vast, meaningless palindrome of code) could easily be compressed, but that would also probably necessitate some kind of indexing so the computer wouldn’t have to skim along the whole code every time to just look for that one thing (then again, some of our cellular machinery is basically doing something like this).
It’s all very complicated and there’s still quite a lot that we don’t know.