The GBS code has been developed in the last few years to simulate plasma dynamics in tokamak SOL conditions. GBS advances the drift-reduced Braginskii equations, solving at the same time the neutral atoms kinetic equation by the method of characteristics. In GBS the plasma dynamics is evolved as the interplay between plasma sources (due to the neutral ionization and the plasma outflow from the tokamak core), turbulent transport, and plasma losses (at the limiter or through recombination processes). Consequently, the code evolve self-consistently the three-dimensional plasma profiles, with no separation between equilibrium and fluctuations. To describe the plasma physics at the magnetic pre-sheath entrance, where the validity of the drift approximation breaks down, a set of boundary conditions have been derived and implemented in GBS. Moreover, the interaction of the plasma with the neutrals is taken self-consistently into account, by evaluating plasma source and energy losses due to ionization events, the drag due to charge-exchange collisions, and the recombination processes. The numerical scheme implemented in GBS has been recently improved, allowing a very efficient treatment of electromagnetic fluctuations, the relaxation of the Bussinesq approximation, and the simulation of increased tokamak sizes. The code verification of GBS was performed by using the method of manufactured solutions, and the simulations have been validated against experimental measurements from several tokamaks worldwide. In the present work we will focus on our recent generalization of the GBS magnetic geometry, in particular we will present the effects of plasma shaping on the SOL turbulence. This research was supported in part by the Swiss National Science Foundation and was carried out within the framework of the EUROfusion Consortium. It received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.