  We introduce a family of linear sets of $\mathrm{PG}(1,q^{2n})$ arising from
maximum scattered linear sets of pseudoregulus type of $\mathrm{PG}(3,q^{n})$.
For $n=3,4$ and for certain values of the parameters we show that these linear
sets of $\mathrm{PG}(1,q^{2n})$ are maximum scattered and they yield new
MRD-codes with parameters $(6,6,q;5)$ for $q>2$ and with parameters $(8,8,q;7)$
for $q$ odd.
