Let $R$ be a ring with identity such that each (right) ideal of $R/J(R)$ is idempotent, where $J(R)$ is the Jacobson radical of $R$. Is $R/J(R)$ necessarily von-Neumann regular?

Certainly, the answer is "yes" in the commutative setting due to the fact that a commutative ring is von-Neumann regular if and only if each ideal of which is idempotent.

Thanks in advance!