Let $R=\oplus_{I\geq 0}R_i$ be a positive graded ring(maybe not commutative), where $R_0$ is a commutative Noetherian ring. If $R$ is finite generated $R_0$-algebra, is $R$ Noetherian?

In here, Is every (left) graded-Noetherian graded ring (left) Noetherian?, $\mathbb Z$-graded ring is graded Noehterian iff it is Noetherian.

I found that this result is true for graded-commutative ring using Artin-Tate lemma:https://en.wikipedia.org/wiki/Artin-Tate_lemma.

Thank you in advance.