Rotating grid turbulence experiments have been carried out in a stably stratified fluid for relatively large Reynolds numbers (mesh Reynolds numbers up to 18000). Under the combined effects of rotation and stratification the flow degenerates into quasi-horizontal motions. This regime is investigated using a scanning imaging velocimetry technique which provides time-resolved velocity fields in a volume. The most obvious effect of rotation is the inhibition of the kinetic energy decay, in agreement with the quasi-geostrophic model which predicts the absence of a direct energy cascade, as found in two-dimensional turbulence. In the regime of small Froude and Rossby numbers, the dynamics is found to be non-dissipative and associated with a symmetric and highly intermittent vertical vorticity field, that displays $k_h^{-3}$ energy spectra. For higher Rossby numbers, fundamental differences with the quasi-geostrophic model are found. A significant decay of kinetic energy, which does not depend on the stratification, is observed. Moreover, in this regime, although both cyclones and anticyclones are initially produced, the intense vortices are only cyclones. For late times the flow consists of an assembly of coherent interacting structures. Under the influence of both rotation and stratification, they take the form of lens-like eddies with aspect ratio proportional to $f/N$.