Interesting... no genes at all? Just curious.
Your red blood cells, for instance. Yeah, I know, you can quibble about mitochondrial DNA, but that misses the point that living cells do not necessarily require DNA to be present in order to survive. It's a question of the cell's needs, what the cell is able to absorb from its environment, and what it has to manufacture for itself. While blood is an unusually hospitable environment to support something as complicated as a red blood cell, the earliest cells probably didn't have very sophisticated needs.