How to argue against the "common design" argument?

The common design argument claims that anatomical and genetic similarities between species are not necessarily evidence for common ancestry and could well be explained by similar design by a higher power. Creationists usually use this argument along with the Coder Analogy, which states that the similarity between the code of two given computer programs are better explained by the share of a common coder than the share of a computer program from which the two programs arose.

Now the question is: how can we eliminate the common design hypothesis?