Let $Y$ be the abelian variety $\mathbb{C}/\mathbb{Z}[i] \times \mathbb{C}/\mathbb{Z}[i] $ where $\mathbb{Z}[i]$ denote the set of Gaussian integers in $\mathbb{C}$. Let $X$ be the quotient of $Y$ by action of the group generated by the map $\eta(x,y)=(ix,iy)$. This group generated is of order 4, and is given by $\{e, -e, \eta, -\eta\}$ where $e$ is the identity map.

How can we show that $X$ is in fact a rational surface and has 10 singularities? I have perused several resources in regarding Kummer surfaces and could not find any literature using such a construction.