  In this paper, we introduce the homogeneous weight and homogeneous Gray map
over the ring $R_{q}=\mathbb{F}_{2}[u_{1},u_{2},\ldots,u_{q}]/\left\langle
u_{i}^{2}=0,u_{i}u_{j}=u_{j}u_{i}\right\rangle$ for $q \geq 2$. We also
consider the construction of simplex and MacDonald codes of types $\alpha$ and
$\beta$ over this ring.
