And, no, it is not possible (today) to rebuild a multi gigabase hexaploid genome. The best that's been done so far is mycoplasma (500kb genome, which is many orders of magnitude smaller).

Also, the "genome sequence" presented here is not really complete. Thus far only the simplest organisms have had their genomes synthesized from a digital template and resulted in a viable cell. We rarely can produce a "complete" genome for anything other than bacteria and viruses. And for those, the diversity in the population makes the idea of establishing a single genome sequence somewhat limiting.

What we can do today is to manipulate DNA and re-inject into an egg. Although not nothing, this is not "just its genome."

In 100 years? Probably.

is it possible to recreate a running program from just it's source?

(lacking a compiler, development and production environments, and perhaps user inputs)

so my feeling is, not really, to an approximation