I have a linear code $C$ over $\mathbb{F}_7$ with generator matrix
\begin{equation*} G=\left[\begin{array}{cccccc} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 3 & 3^2 & 3^3 & 3^4 & 3^5 \end{array}\right] \end{equation*}
I know that this is a Reed-Solomon code, and I'm trying to find the generator polynomial of $C$ without using this fact. I know that $3$ is a primitive element of $\mathbb{F}_7$, and I've shown that $C$ is a cyclic code, since the shifts of the rows of $G$ are still codewords.
Now I'm stuck, and not sure how to proceed with finding the generator polynomial without somehow making row operations on $G$ and "making it appear" in the standard cyclic form.