  In this short note we construct an embedding of the planar algebra for
$\overline{\operatorname{Rep}(U_q(sl_3))}$ at $q = e^{2\pi i \frac{1}{24}}$
into the graph planar algebra of di Francesco and Zuber's candidate graph
$\mathcal{E}_4^{12}$. Via the graph planar algebra embedding theorem we thus
construct a rank 11 module category over
$\overline{\operatorname{Rep}(U_q(sl_3))}$ whose graph for action by the vector
representation is $\mathcal{E}_4^{12}$. This fills a small gap in the
literature on the construction of $\overline{\operatorname{Rep}(U_q(sl_3))}$
module categories. As a consequence of our construction, we obtain the
principal graphs of subfactors constructed abstractly by Evans and Pugh.
