Nature is more complex than the most complex computer program.
Why should it be surprising that DNA figures into the extremely complex, intricate, and highly developed patterns of the natural world?
So how do you explain the appearance of DNA and its encoding information?
Was it by "random" bonding of sugars, phosphates and nucleobases? Or were these chemicals bonded together by some mysterious, naturally "directed" process?
The odds would be impossible for the former to be true, and science can even come close to an explanation for the latter.
As to your question, it is not surprising that DNA figures into our complex world. In fact, its a requirement for the existence of life. The question that really needs to be answered is: "If life originated naturally, how do you explain the appearance of DNA"?