  This paper investigates the construction of rank-metric codes with specified
Ferrers diagram shapes. These codes play a role in the multilevel construction
for subspace codes. A conjecture from 2009 provides an upper bound for the
dimension of a rank-metric code with given specified Ferrers diagram shape and
rank distance. While the conjecture in its generality is wide open, several
cases have been established in the literature. This paper contributes further
cases of Ferrers diagrams and ranks for which the conjecture holds true. In
addition, the proportion of maximal Ferrers diagram codes within the space of
all rank-metric codes with the same shape and dimension is investigated.
Special attention is being paid to MRD codes. It is shown that for growing
field size the limiting proportion depends highly on the Ferrers diagram. For
instance, for $[m\times 2]$-MRD codes with rank~$2$ this limiting proportion is
close to $1/e$.
