We present the methodology and performance of the new Lagrangian hydrodynamics code MAGMA2, a Smoothed Particle Hydrodynamics code that benefits from a number of non-standard enhancements. It uses high-order smoothing kernels and wherever gradients are needed, they are calculated via accurate matrix inversion techniques. Our default version does not make use of any kernel gradients, but a more conventional formulation has also been implemented for comparison purposes. MAGMA2 uses artificial viscosity, but enhanced by techniques that are commonly used in finite volume schemes such as reconstruction and slope limiting. While simple to implement, this approach efficiently suppresses particle noise, but at the same time drastically reduces dissipation in locations where it is not needed and actually unwanted. We demonstrate the performance of the new code in a number of challenging benchmark tests including e.g. complex, multi-dimensional Riemann problems and more astrophysical tests such as a collision between two stars to demonstrate its robustness and excellent conservation properties.