We enumerate three classes of non-medial quasigroups of order 243=35 up to
isomorphism. There are 17004 non-medial trimedial quasigroups of order 243
(extending the work of Kepka, B\'en\'eteau and Lacaze), 92 non-medial
distributive quasigroups of order 243 (extending the work of Kepka and
N\v{e}mec), and 6 non-medial distributive Mendelsohn quasigroups of order
243 (extending the work of Donovan, Griggs, McCourt, Opr\v{s}al and
Stanovsk\'y).
The enumeration technique is based on affine representations over commutative
Moufang loops, on properties of automorphism groups of commutative Moufang
loops, and on computer calculations with the \texttt{LOOPS} package in
\texttt{GAP}