Question 13Equilateral $\triangle ABC$ has side length $\sqrt{111}.$ There are four distinct triangles $AD_1E_1,$ $AD_1E_2,$ $AD_2E_3,$ and $AD_2E_4,$ each congruent to $\triangle ABC,$ with $BD_1 = BD_2 = \sqrt{11}.$ Find $\sum_{k=1}^{4}(CE_k)^2.$