Well, the DNA itself probably wouldn't be enough because it doesn't really encode an algorithm or recipe describing how a (multicellular in this context) living organism is constructed from it's genetic information. Instead, the DNA is more like a huge collection of building blocks. But how and what will be constructed from this pile (meaning what will be included in the final system and what won't) that's a completely different matter.

A few links for the interested: https://en.wikipedia.org/wiki/Developmental_biology http://en.wikipedia.org/wiki/Epigenetics

That said, there has been quite an exciting paper published around a year ago describing the first simulation of one life cycle of an in silico Mycoplasma genitalium (the smallest known bacteria). Here's a link to relevant HN discussion: https://news.ycombinator.com/item?id=4272039