  We consider a nilpotent Lie group with a bracket-generating distribution
$\hhh$ and an asymmetric left-invariant norm $\|\cdot\|_K$ induced by a convex
body $K\subseteq\hhh$ containing $0$ in its interior. In this paper we prove
the existence of minimizers of the perimeter functional $P_K$ associated to
$\|\cdot\|_K$ under a volume (Haar measure) constraint. Our result generalizes
the one of Leonardi and Rigot for Carnot groups.
