  In this paper, we count the number of matrices whose rows generate different
$\mathbb{Z}_2\mathbb{Z}_8$ additive codes. This is a natural generalization of
the well known Gaussian numbers that count the number of matrices whose rows
generate vector spaces with particular dimension over finite fields. Due to
this similarity we name this numbers as Mixed Generalized Gaussian Numbers
(MGN). The MGN formula by specialization leads to the well known formula for
the number of binary codes and the number of codes over $\mathbb{Z}_8,$ and for
additive $\mathbb{Z}_2\mathbb{Z}_4$ codes. Also, we conclude by some properties
and examples of the MGN numbers that provide a good source for new number
sequences that are not listed in The On-Line Encyclopedia of Integer Sequences.
