We discuss covariant quantum spaces as solutions of the IKKT or IIB matrix model with mass term. This leads to a ghost-free higher-spin gauge theory, which contains all degrees of freedom for gravity. The gravitational sector can be understood in terms of an effective frame and an associated connection. The resulting covariant equations of motion of the classical model are discussed, which can be interpreted as pre-gravity, having 2 derivatives less than the Einstein-Hilbert action. The latter is recovered upon including the 1-loop effective action. This provides a new formulation of gravity which is intrinsically quantum.