Expanding the SETI initiative to seek intelligent data within DNA sequences?
Let's extend your idea a bit... Ok, there are conserved sequences that we may not know what their function is. Let's assume that they are indeed not functional and are some kind of message left by an ancient form of intelligence.

How would you go about detecting that? It is already given that they are highly non-random, but this is not surprising and many "non-message" sequences have this property. Also consider that these sequences are quite short, meaning that they will have low information content. This means that if you check enough conversion codes and use imagination, you would probably be able to find several "messages" which are "hidden" there (e.g. "bible codes" etc). In other words, as I am a scientist that deals with probability and pattern recognition frequently, you will have a very hard time trying to convince me that you found a real hidden message... Formally, you don't have a satisfying background model.

The main difference from SETI is that there they know that their background is essentially random noise, so it is much easier to detect "intelligent" messages.