Most non-coding DNA does have a regulatory purpose. Things like copy number variations (where information is "duplicated") between promoters and enhancers can can change the rate at which particular genes get transcribed. This is my point: that viewing the genome as "information" in the simple sense of each ATCG nucleotide corresponding to bits is absurd. The genome is a geometric AND chemical entity and encodes information using both paradigms.
My point is not to say that you are wrong, but rather that you do not know. It is FAR from well established that the genome is inefficient at storing information.