Singular Values & the SVD · Superchallenge problem

Let $M = I_4 + J_4$, where $J_4$ is the $4\times 4$ all-ones matrix. Find the minimum of $\|M - B\otimes C\|_F$ over all real $2\times 2$ matrices $B$ and $C$ (here $\otimes$ is the Kronecker product). Give an exact answer.