Particle shape representation is a fundamental problem in the Discrete Element Method (DEM). Spherical particles with well known contact force models remain popular in DEM due to their relative simplicity in terms of ease of implementation and low computational cost. However, in real applications particles are mostly non-spherical, and more sophisticated particle shape models, like superquadric shape, must be introduced in DEM. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylinder-like and box(dice)-like particles just varying five shape parameters. In this study we present an efficient C++ implementation of superquadric particles within the open-source and parallel DEM package LIGGGHTS. To reduce computational time several ideas are employed. In the particleparticle contact detection routine we use the minimum bounding spheres and the oriented bounding boxes to reduce the number of potential contact pairs. For the particlewall contact an accurate analytical solution was found. We present all necessary mathematics for the contact detection and contact force calculation. The superquadric DEM code implementation was verified on test cases such as angle of repose and hopper/silo discharge. The simulation results are in good agreement with experimental data and are presented in this paper. We show adequacy of the superquadric shape model and robustness of the implemented superquadric DEM code.