The purpose of this paper is twofold. First, we present the extension of the Liège intranuclear-cascade model to reactions induced by light ions. We describe here the ideas upon which we built our treatment of nucleus-nucleus reactions and we compare the model predictions against a vast set of heterogeneous experimental data. In spite of the discussed limitations of the intranuclear-cascade scheme, we find that our model yields valid predictions for a number of observables and positions itself as one of the most attractive alternatives available to GEANT4 users for the simulation of light-ion-induced reactions. Second, we describe the C++ version of the code, which is physicswise equivalent to the legacy version, is available in GEANT4, and will serve as the basis for all future development of the model.