Arbitrariness in the genetic code is one of the main reasons for a linguistic approach to molecular biology: the genetic code is usually understood as an arbitrary relation between amino acids and nucleobases. However, from a semiotic point of view, arbitrariness should not be the only condition for definition of a code, consequently it is not completely correct to talk about "code" in this case. Yet we suppose that there exist a code in the process of protein synthesis, but on a higher level than the nucleic bases chains. Semiotically, a code should be always associated with a function and we propose to define the genetic code not only relationally (in basis of relation between nucleobases and amino acids) but also in terms of function (function of a protein as meaning of the code). Even if the functional definition of meaning in the genetic code has been discussed in the field of biosemiotics, its further implications have not been considered. In fact, if the function of a protein represents the meaning of the genetic code (the sign's object), then it is crucial to reconsider the notion of its expression (the sign) as well. In our contribution, we will show that the actual model of the genetic code is not the only possible and we will propose a more appropriate model from a semiotic point of view.