  We consider linear rank-metric codes in $\mathbb F_{q^m}^n$. We show that the
properties of being MRD (maximum rank distance) and non-Gabidulin are generic
over the algebraic closure of the underlying field, which implies that over a
large extension field a randomly chosen generator matrix generates an MRD and a
non-Gabidulin code with high probability. Moreover, we give upper bounds on the
respective probabilities in dependence on the extension degree $m$.
