I think you would be interested in this book: http://www.amazon.com/Language-God-Scientist-Presents-Evidence/dp/0743286391
This is written by the head of the human genome project. He basically agrees with your point of view. But since he is a real scientist in this area he can answer you question the best.
And don't listen to all these people just saying no, you're stupid. They are neither scientists nor religious people. They are illiterate in both spheres and just like to lash out at people because it gives them some sense of pleasure. Just backgroud noise.
OK, I'll take a stab. I have worked with protein folding modeling. This is the science of trying to understand how a certain sequence of amino acids will lead to a specific molecule shape that will then act a certain way and have a certain function in the cell and in the body. This understanding is required in order to make sense of how the gene sequence functions to effect the organism. Without knowledge of how the protein folds we can't say what effect the alteration of one gene would be or how one gene is expressed in the body.
I find that the problem is profoundly intractable. The mechanisms are far too complex. In fact, there appear to be helper proteins that show up at certain times in the folding process that altar the outcome. Thus the process of gene expression is so complex that it involves other molecules other than just the amino acid chain. It is my opinion that the understanding of how a gene expresses itself in the organism cannot be known to us. It is literally like frying an egg and trying to figure out where evey strand of protein will end up, and then trying to take the scrambled eggs and untie them to form an egg again and make one small change to cause it to form into a different shaped ball of scrambled eggs.
Because of this complexity, the language of DNA is simply unkown to us. We may know the letters, but we can't read the book. All we have done is identify what the letters are (the human genome) but we have no idea what it means because we don't speak the language. We know a few words (a few diseases that are known to have a specific genetic cause).
Thus I don't buy that we can identify the code that makes life possible. The code must also contain the process that cause the expression of the genes, which we don't understand. Therefore, the argument that the code proves God is moot.