Galois group over $F_9$

Question

I am trying to compute the Galois group of the polynomial $f(x)=x^4+2x^2-2$ over $F_3$ and $F_9$. I see that $f(x)$ is reducible over $F_3[x]$, $f(x)=(x^2+1)^2$, therefore we have that the Galois group over $F_3$ is $\mathbb{Z}_2$. But I have no idea about the Galois group over $F_9$. Can someone give me some hint?