  We propose a physical model to describe the mechanisms of two major scenarios
of the genetic code evolution, the codon capture and ambiguous intermediate
scenarios, in a consistent manner. We sketch the lowest dimensional version of
our model, a minimal model, by introducing a physical quantity, codon level. On
the basis of the hierarchical structure of the codon levels two scenarios are
classified into two different routes of the evolutional process. In the case of
the ambiguous intermediate scenario we perform a simulation implemented cost
selection of amino acids and confirm a rapid transition of the code change.
Such rapidness reduces uncomfortableness of the non-unique translation of the
code at intermediate state that is the weakness of the scenario.
