  The tensor rank of some Gabidulin codes of small dimension is investigated.
In particular, we determine the tensor rank of any rank metric code equivalent
to an $8$-dimensional $\mathbb{F}_q$-linear generalized Gabidulin code in
$\mathbb{F}_{q}^{4\times4}$. This shows that such a code is never minimum
tensor rank. In this way, we detect the first infinite family of Gabidulin
codes which are not minimum tensor rank.
