Weight distributions of a class of skew cyclic codes over $M_2({\mathbb{F}}_2)$

Let $M_2({\mathbb{F}}_2)$ be the ring of matrices of order $2\times 2$ over finite field ${\mathbb{F}}_2$ and $\omega \in M_2({\mathbb{F}}_2)$ be a cubic primitive root of unity. For any even positive integer $t$, the weight distributions of the skew cyclic codes of length $3t$ with parity check polynomials $x^t-{\omega }^i,i=0,1,2$ and $(x^t-{\omega }^j)(x^t-{\omega }^k)$, $0\le j<k\le 2$ were determined.