The Busy Beaver is an interesting theoretical problem proposed by Rado in 1962, in the context of the existence of non computable functions. In this paper we propose an evolutionary approach to this problem. We will focus on the representational issues, proposing alternative ways of codifying and interpreting Turing Machines, designed to take advantage of the existence of sets of equivalent Turing Machines. The experimental results show that these alternatives provide improvement over the “standard” genetic codification.