The systole of a compact non simply connected Riemannian manifold is the smallest length of a non-contractible closed curve ; the systolic ratio is the quotient $\mathrm{volume}/(\mathrm{systole})^n $. Its infimum, on the set of all the riemannian metrics, is known to be positive for a large class of manifolds, including the $K(\pi,1)$. We study the optimal systolic ratio of compact, $3$-dimensional non orientable Bieberbach manifolds, and prove that it cannot be realized by a flat metric.