Accurate modeling of sea ice dynamics is a major challenge, but also a key requirement for forecasting its future evolution and assessing its impact on climate change. The sea-ice model neXtSIM is specifically designed for this purpose, relying on a Lagrangian framework to accurately capture highly localized features such as leads and ridges, which likely play an important role in controlling the energy exchanges at the interfaces of the atmosphere-ice-ocean coupled system. Despite a parallelisation effort a few years ago, several components of the code, which are intrinsically required by a Lagrangian framework, such as the remeshing procedure, remained sequential, which created significant bottlenecks that limited the model's overall capabilities. To tackle this problem, we further developed the parallel anisotropic mesh adaptation tool ParMMG2D, which demonstrates excellent scalability up to 512 processors with 20 million elements. This tool has been integrated within neXtSIM to enable parallel remeshing, currently limited to homogeneous isotropic meshes. In addition, parallelization of subsequent interpolation, output writing, and drifting buoy tracking has also been achieved. Together, these improvements now enable kilometer-scale simulations within a reasonable timeframe: a one-year simulation with 2 km elements takes only a few days, while a full season with 1 km elements can be simulated in about a week on 128 processors. Therefore, neXtSIM now stands out as cutting-edge software for simulating highly resolved sea ice dynamics, combining the accuracy of a Lagrangian framework with high computational efficiency.