  The first nonlinear gyrokinetic simulations obtained using a moment approach
based on the Hermite-Laguerre decomposition of the distribution function are
presented, implementing advanced models for the collision operator. Turbulence
in a \modif{two-dimensional} Z-pinch is considered within a flux tube
configuration. In the collisionless regime, our gyromoment approach shows very
good agreement with nonlinear simulations carried out with the continuum
gyrokinetic code GENE, even with fewer gyromoments than required for the
convergence of the linear growth rate. By using advanced linear collision
operators, the role of collisions in setting the level of turbulent transport
is then analyzed. The choice of collision operator model is shown to have a
crucial impact when turbulence is quenched by the presence of zonal flows. The
convergence properties of the gyromoment approach improve when collisions are
included.
