  We study the construction of complex minimal smooth surfaces $S$ of general
type with $p_g(S)=0$ and $K_S^2=7$. Inoue constructed the first examples of
such surfaces, which can be described as Galois
$\mathbb{Z}_2\times\mathbb{Z}_2$-covers over the four-nodal cubic surface.
Later the first named author constructed more examples as Galois
$\mathbb{Z}_2\times\mathbb{Z}_2$-covers over certain six-nodal del Pezzo
surfaces of degree one.
  In this paper we construct a two-dimensional family of minimal smooth
surfaces of general type with $p_g=0$ and $K^2=7$, as Galois
$\mathbb{Z}_2\times\mathbb{Z}_2$-covers of certain rational surfaces with
Picard number three, with eight nodes and with two elliptic fibrations. This
family is different from the previous ones.
