Developing open-source foundation models is essential for advancing research in music audio understanding and ensuring access to powerful, multipurpose representations for music information retrieval. We present OMAR-RQ, a model trained with self-supervision via masked token classification methodologies using a large-scale dataset with over 330,000 hours of music audio. We experiment with different input features and quantization options, and achieve state-of-the-art performance in music tagging, pitch estimation, chord recognition, beat tracking, segmentation, and difficulty estimation among open self-supervised models. We open-source our training and evaluation pipelines and model weights, available at https://github.com/mtg/omar-rq.