  In this paper, we consider a Finsler space with a Randers change of Quartic
metric F = $\sqrt[4]{\alpha^4 + \beta^4} + \beta$. The conditions for this
space to be with reversible geodesics are obtained. Further, we study some
geometrical properties of F with reversible geodesics and prove that the
Finsler metric F induces a generalized weighted quasi-distance $d_F$ on M.
