Two forces are in general, hypothesized to have influenced the origin of the organization of the genetic code: the physicochemical properties of amino acids and their biosynthetic relationships. In view of this, we have considered a model incorporating these two forces. In particular, we have studied the optimization level of the physicochemical properties of amino acids in the set of amino acid permutation codes that respects the biosynthetic relationships between amino acids. Where the properties of amino acids are represented by polarity and molecular volume we obtain indetermination percentages in the organization of the genetic code of approximately 40%. This indicates that the contingent factor played a significant role in structuring the genetic code. Furthermore, this result is in agreement with the genetic code coevolution hypothesis, which attributes a merely ancillary role to the properties of amino acids while it suggests that it was their biosynthetic relationships that organized the code. Furthermore, this result does not favor the stereochemical models proposed to explain the origin of the genetic code. On the other hand, where the properties of amino acids are represented by polarity alone, we obtain an indetermination percentage of at least 21.5%. This might suggest that the polarity distances played an important role and would therefore provide evidence in favor of the physicochemical hypothesis of genetic code origin. Although, overall, the analysis might have given stronger support to the latter hypothesis, this did not actually occur. The results are therefore discussed in the context of the different theories proposed to explain the origin of the genetic code.