A two-dimensional code is defined as a set of rectangular pictures over an alphabet $\varSigma $ such that any picture over $\varSigma $ is tilable in at most one way with pictures in X. It is in general undecidable whether a set of pictures is a code, even in the finite case. Recently, finite strong prefix codes were introduced in [3] as a family of decidable picture codes. In this paper we study infinite strong prefix codes and give a characterization for the maximal ones based on iterated extensions. Moreover, we prove some properties regarding the measure of these codes.