When homogeneous coordinate ring of an Abelian variety is Gorenstein?

Question

Let $A$ be an abelian variety of dimension at least $2$. If $A$ is embedded into a projective space by a very ample line bundle $\mathcal{L}$ under which assumptions on $\mathcal{L}$ the homogeneous coordinate ring $$ R = \oplus_{i \geq 0} H^0(A, \mathcal{L}^i) $$ of $A$ is a graded Gorenstein ring?