  We find a one-parameter family of non-isomorphic nilpotent Lie algebras
$\mathfrak{g}_a$, with $a \in [0,\infty)$, of real dimension eight with
(strongly non-nilpotent) complex structures. By restricting $a$ to take
rational values, we arrive at the existence of infinitely many real homotopy
types of $8$-dimensional nilmanifolds admitting a complex structure. Moreover,
balanced Hermitian metrics and generalized Gauduchon metrics on such
nilmanifolds are constructed.
