  In this paper, we present a new family of maximum rank distance (MRD for
short) codes in $\mathbb F_{q}^{2n\times 2n}$ of minimum distance $2\leq d\leq
2n$. In particular, when $d=2n$, we can show that the corresponding semifield
is exactly a Hughes-Kleinfeld semifield. The middle and right nuclei of these
MRD codes are both equal to $\mathbb F_{q^n}$. We also prove that the MRD codes
of minimum distance $2<d<2n$ in this family are inequivalent to all known ones.
The equivalence between any two members of this new family is also determined.
