bioinformatics - Generating custom human DNA sequences based on traits such as eye colour?

I'm wondering if it would be possible to create software (unless some already exists, but I couldn't find any) to generate human DNA (the base pairs on the double helix) containing genes representing specific permutations (eye colour, hair colour, etc.)?

Basically, something like the "character builder" from those "Saints Row"-style video games, except with actual human chromosomes, enabling you to essentially create a 'custom' human.

Of course, that is assuming that all human DNA has a common structure, and that the entire sequence can either be assembled from individual chromosomes, or by using a reference genome and modifying specific genes/chromosomes according to user input. Is this the case?

One setback here, of course, could be the number of bases in each chromosome, which ranges between 100 million and 250 million, and the (approximately) 23000 human genes - a lot of data to manipulate.