  Recently, Pennisi and Ruggeri [J Stat Phys 179, 231-246 (2020)] consider the
classical limit of the relativistic theory of moments associated with the
Boltzmann-Chernikov equation truncated at a tensorial index $N+1$ and they
proved that there exists a unique possible choice of the moments in the
classical case for a given $N$ both for monatomic and polyatomic gases. In
particular, in polyatomic gases, there exists a new hierarchy of moments that
is more general than the one considered in the recent literature. As
consequence, when $N=2$, in the classical limit, there is a theory with $15$
fields. In this paper, we consider this system of moments, and we close the
system using the maximum entropy principle. It is shown that the theory
contains as a principal subsystem the previously polyatomic $14$ fields theory,
and in the monatomic limit, in which the dynamical pressure vanishes, the
differential system converges instead to Grad 13-moments system to the 14
moments theory proposed by Kremer [Annales de l'I.H.P. Physique th\'eorique,
45, 419-440 (1986)].
