Our work aims at providing accurate numerical solutions of the Navier-Stokes equations at practical engineering scales, with minimal modeling of the sub grid dynamics. To this end we developed a new computer code maDG designed for the efficient parallel implicit solution of the three-dimensional un-structured nodal discontinuous Galerkin discretization of the unsteady compressible Navier-Stokes equations. The code has been developed at Princeton University by the authors to provide an efficient, modular, and maintainable software platform enabling algorithmic and modeling studies in high-resolution CFD. Computational efficiency is achieved by using efficient numerical methods for implicit time integration of discontinuous Galerkin discretization based on Jacobian-free Newton-Krylov methods, which have been demonstrated to be significantly more efficient than explicit methods from toy problems up to industrial scale simulations. The software design philosophy of maDG reflects the motivation to create a tool suitable for assessing the relative merits of different algebraic solution methods, time integration schemes, and spatial discretization approaches in the context of high performance parallel computing. To this end, the code is highly modular with most components being interchangeable; the same solvers used for the three-dimensional DG discretization of the compressible Navier-Stokes equations on large clusters also work transparently for a serial 1D finite volume discretization of the Poisson equation. The software implementation in maDG is designed to exploit the capabilities of large HPC systems; the current version leverages RAJA for GPU execution and OpenMP for shared memory CPU parallelization, or pure C++ for single-threaded CPU execution, in such a way that the backend is abstracted from the main code. Results obtained for the tandem spheres, a recent benchmark problem for high-order methods, represent both the highest resolution known to have been performed as well as at higher Reynolds numbers. Additionally, results obtained for the high lift Common Research model will be presented to illustrate the current capability of our approach.