This work presents recent advances made in the flow solver CODA (CFD solver jointly developped by ONERA, DLR and Airbus) as regards its high-order spatial discretization, namely based on modal Discontinuous Galerkin and nodal, entropy stable DGSEM schemes. We present the high-order DG and DGSEM shock capturing strategy employed in CODA, as well as several applications, including an inviscid forward-facing step at Mach 3, a viscous shock-wall interaction, and the supersonic Taylor-Green vortex flow. Theses tests are carried out using various mesh topologies and polynomial degrees, which demonstrate the robustness, flexibility and accuracy of CODA for such applications. The interest of the DG method is also demonstrated in a more applied cruising-condition CRM configuration using RANS modeling. In this case, a significant improvement in the drag coefficient prediction are observed when increasing the order of accuracy or polynomial degree of the DG approximation. Using DGSEM, we demonstrate the capability to perform a wall-modelled LES of the subsonic flow around a rudimentary landing gear geometry placed inside a wind tunnel, employing meshes generated in a highly automatic manner. We assess accuracy in the mean and standard deviation of the pressure coefficient along the wheel's circumference and find an overall good match with experimental results.