A submanifold M of a K\"ahler manifold $(\bar{M},J)$ is said to be CR if its tangent space orthogonally splits into holomorphic ($J\mathcal{D} \subset \mathcal{D}$) and antiholomorphic ($J\mathcal{D}^\perp \subset (TM)^\perp$) distributions. The antiholomorphic distribution of a CR submanifold is always integrable. We discuss some inhomogeneous minimal submanifolds of $\mathbb{C}P^n$ that occur as CR submanifolds for which the antiholomorphic foliation forms an equidistant $\mathbb{R}P^7$-fibration over a K\"ahler-Einstein manifold and carries a Yang-Mills connection and associated Einstein geometries.