Here's an online database of difference sets including non-cyclic, abelian cases: ccrwest.org/diffsets.html I checked the case $\vert D \vert < 150$, only to find one (possible) example over (\mathbb{Z}/n\mathbb{Z})^2. It says $PG(4,3)$ gives a $(121,40,13)$ difference set over (\mathbb{Z}/11\mathbb{Z})^2, but I thought it should be a "cyclic" one (i.e., over the cyclic group of order $121$). So, unless I'm missing something, it's an error, and if that's the case, there seems to be no known small example. In any case, such difference sets seem to be very rare if there's one at all.