Is genetic code redundancy related to retention of structural information in both DNA strands?

We have noted that the sense-antisense relationships inherent in the genetic code divide the amino acids into three separate groups. The nature of the amino acids in each group may allow the polypeptides coded by the antisense strand to retain the secondary structure patterns of the translated strand. Also, this relationship requires all but eight of the codons in the eukaryotic code and all but four in the mitochondrial code. Thus, genetic code redundancy could be related to evolutionary pressure toward retention of protein structural information in both strands of DNA.