  An almost complex manifolds $(M^4,J)$ of real dimension 4 with non-degenerate
torsion bundle admit a double absolute parallelism and it is provided the
classification of homogeneous $(M^4,J)$ having an associated non-solvable Lie
algebra. We extend such a classification to the analysis of the manifolds
having an associated solvable Lie algebra, up-to-coverings. Moreover, for
homogeneous $(M^4,J)$ we provide examples with connected and non-connected
double covering, thus proving that in general the double absolute parallelism
is not the restriction of two absolute parallelisms. Furthermore, it is given
the definition of a natural metric induced by the absolute parallelisms on
$(M^4,J)$ and an example of an almost complex manifold with non-degenerate
torsion endowed with that metric such that it becomes an almost K\"ahler
manifold.
