We study a finite-dimensional algebra $\Lambda$ constructed from a Postnikov diagram $D$ in a disk, obtained from the dimer algebra of Baur-King-Marsh by factoring out the ideal generated by the boundary idempotent. Thus, $\Lambda$ is isomorphic to the stable endomorphism algebra of a cluster tilting module $T\in\operatorname{CM}(B)$ introduced by Jensen-King-Su in order to categorify the cluster algebra structure of $\mathbb{C}[\operatorname{Gr}_{k}(\mathbb{C}^n)]$. We show that $\Lambda$ is self-injective if and only if $D$ has a certain rotational symmetry. In this case, $\Lambda$ is the Jacobian algebra of a self-injective quiver with potential, which implies that its truncated Jacobian algebras in the sense ofHerschend-Iyama are 2-representation finite. We study cuts and mutations of such quivers with potential leading to some new 2-representation finite algebras.