Straw man. Most genome changes are not the result of nor rely on random mutation, though you would be correct that random mutation is a pretty damn slow. Some of the other mechanisms provide smooth and rapid DNA drift, which almost certainly dominates evolutionary variation in most complex organisms.
What other mechanisms? That sounds interesting. If it isn't random, doesn't Darwinian evolution go out the window? I know many evolutionists retort that "Darwinism" has long been replaced, but they continue to use the term in all kind of contexts and only seem to suggest that when holes in Darwinistic theories are pointed out. Still, I'm always intrigued by theories of non-random mutation.
Perhaps I was using the term "genome" in too broad a sense. But my point is, the complexity of the human organism is highly unlikely to have evolved (I won't say couldn't have, because though the statistical argument is compelling, I don't know that that kind of proof can be considered conclusive)as the result of random mutation followed by natural selection. I think the current state of life is the result of evolution, I just don't think it is or was random. I think life has been programmed to evolve.