Explainable Artificial Intelligence (xAI) has the potential to enhance the transparency and trust of AI-based systems. Although accurate predictions can be made using Deep Neural Networks (DNNs), the process used to arrive at such predictions is usually hard to explain. In terms of perceptibly human-friendly representations, such as word phrases in text or super-pixels in images, prototype-based explanations can justify a model's decision. In this work, we introduce a DNN architecture for image classification, the Enhanced Prototypical Part Network (EPPNet), which achieves strong performance while discovering relevant prototypes that can be used to explain the classification results. This is achieved by introducing a novel cluster loss that helps to discover more relevant human-understandable prototypes. We also introduce a faithfulness score to evaluate the explainability of the results based on the discovered prototypes. Our score not only accounts for the relevance of the learned prototypes but also the performance of a model. Our evaluations on the CUB-200-2011 dataset show that the EPPNet outperforms state-of-the-art xAI-based methods, in terms of both classification accuracy and explainability