The standard genetic code (SGC) is a set of rules according to which 64 codons are assigned to 20 canonical amino acids and stop coding signal. As a consequence, the SGC is redundant because there is a greater number of codons than the number of encoded labels. This redundancy implies the existence of codons that encode the same genetic information. The size and organization of such synonymous codon blocks are important characteristics of the SGC structure whose evolution is still unclear. Therefore, we studied possible evolutionary mechanisms of the codon block structure. We conducted computer simulations assuming that coding systems at early stages of the SGC evolution were sets of ambiguous codon assignments with high entropy. We included three types of reading systems characterized by different inaccuracy and pattern of codon recognition. In contrast to the previous study, we allowed for evolution of the reading systems and their competition. The simulations performed under minimization of translational errors and reduction of coding ambiguity produced the coding system resistant to these errors. The reading system similar to that present in the SGC dominated the others very quickly. The survived system was also characterized by low entropy and possessed properties similar to that in the SGC. Our simulation show that the unambiguous SGC could emerged from a code with a lower level of ambiguity and the number of tRNAs increased during the evolution.