Grid maps obtained from fused sensory information are nowadays among the most popular approaches for motion planning for autonomous driving cars. In this paper, we introduce Deep Grid Net (DGN), a deep learning (DL) system designed for understanding the context in which an autonomous car is driving. DGN incorporates a learned driving environment representation based on Occupancy Grids (OG) obtained from raw Lidar data and constructed on top of the Dempster-Shafer (DS) theory. The predicted driving context is further used for switching between different driving strategies implemented within EB robinos, Elektrobit's Autonomous Driving (AD) software platform. Based on genetic algorithms (GAs), we also propose a neuroevolutionary approach for learning the tuning hyperparameters of DGN. The performance of the proposed deep network has been evaluated against similar competing driving context estimation classifiers.