modular arithmetic - Construction of multiplication and addition tables for GF(4) with Modulo ($x^2 + x + 1$)

I am still trying to understand polynomial arithmetic with Galois Field.
Can someone explain to me what this question is asking to be constructed. I have searched all over google for GF(4) with modulo and I am not getting anywhere.

I have read over a few of the other posts here on the forums but none seem to apply to my specific situation. Can anyone help me understand GF with modulo of a polynomial?

Thanks in advance.