DNA is information about something, so it is mutual information between the code and the environment. If maximizing entropy were the only goal, then generating DNA with a random process would be enough to make evolution happen. This is why entropy is not the sort of information we are talking about here. It is only half of the equation:
H(X) = I(X;Y) + H(X|Y)
If you are really hung up on the word “information,” then we’ll just call the quantity “blarb”, which is the mutual information between DNA and environment.
My claim is evolution cannot generate blarb.