We prove if R is a commutative noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein at, then the class of Gorenstein injective modules is covering. We also prove that over such a ring the class of Gorenstein injective modules is enveloping. In particular this shows the existence of the Gorenstein injective envelopes over commutative noetherian rings with dualizing complexes. This is joint work with Edgar Enochs.