  We extend the notion of super-Minkowski space-time to include
$\mathbb{Z}_2^n$-graded (Majorana) spinor coordinates. Our choice of the
grading leads to spinor coordinates that are nilpotent but commute amongst
themselves. The mathematical framework we employ is the recently developed
category of $\mathbb{Z}_2^n$-manifolds understood as locally ringed spaces. The
formalism we present resembles $\mathcal{N}$-extended superspace (in the
presence of central charges), but with some subtle differences due to the
exotic nature of the grading employed.
