  In this paper, we construct Kleinian groups
$\Gamma<\mathrm{Isom}(\mathbb{H}^{2n})$ from the direct product of $n$ copies
of the rank 2 free group $F_2$ via strict hyperbolization. We give a
description of the limit set and its topological dimension. Such construction
can be generalized to other right-angled Artin groups.
