  We present a $q$-analog of the super Catalan number $(2m)!(2n)!/2m!n!(m+n)!$,
which also generalizes the $q$-Catalan numbers $c_n(\lambda)$, due to
F\"urlinger and Hofbauer, for $\lambda=0$ and $\lambda=1$. We give a
combinatorial interpretation for this analog when $m=2$.
