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We enumerate three classes of non-medial quasigroups of order $243=3^5$ up toisomorphism. There are $17004$ non-medial trimedial quasigroups of order $243$(extending the work of Kepka, B\'en\'eteau and Lacaze), $92$ non-medialdistributive quasigroups of order $243$ (extending the work of Kepka andN\v{e}mec), and $6$ non-medial distributive Mendelsohn quasigroups of order$243$ (extending the work of Donovan, Griggs, McCourt, Opr\v{s}al andStanovsk\'y).  The enumeration technique is based on affine representations over commutativeMoufang loops, on properties of automorphism groups of commutative Moufangloops, and on computer calculations with the \texttt{LOOPS} package in\texttt{GAP}.

Distributive and trimedial quasigroups of order 243