$\mathbb{Z}[i] /\langle 3+3 i\rangle \cong \mathbb{F}_{3}[X] /\left\langle X^{2}+1\right\rangle \times \mathbb{F}_{2} $
Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime