Even if every star in every galaxy in the universe had a duplicate earth, there wouldn't be enough disks & tape on all of them combined to store all the progeny of 1000 generations of a single 1000-codon sequence.

Taking a 1000-codon sequence through one possible lineage for 1000 generations takes maybe a millisecond, so you could fill a disk with possible end points very quickly.

But without some selection criteria, any single lineage of random mutations is as likely as any other, so there is nothing to be learnt from statistically sampling the final generation. All you'd be testing is the distribution of your source of randomness.

So the question becomes, what were you hoping to learn from the outcome of this experiment? If we knew what you were hoping to investigate, we might be able to suggest plausible approaches.