Consider $R=\mathbb{C}[[x]][\frac{d}{dx}]$ as a graded ring (assign $x$ zero weight, and $\frac{d}{dx}$ some non-zero weight). Are there some $A_n$-ring spectra naturally arising in homotopy theory such that $\pi_*X\approx R$?

P.S.: the answer should depend on the weight assigned to $\frac{d}{dx}$. I am not sure what the weight should be (most probably either 1 or 2). I also do not mind adjoining the inverse of $\frac{d}{dx}$ if that is necessary.