AI Foundation models are gaining traction in various applications, including medical fields like radiology. However, medical foundation models are often tested on limited tasks, leaving their generalisability and biases unexplored. We present RayDINO, a large visual encoder trained by self-supervision on 873k chest X-rays. We compare RayDINO to previous state-of-the-art models across nine radiology tasks, from classification and dense segmentation to text generation, and provide an in depth analysis of population, age and sex biases of our model. Our findings suggest that self-supervision allows patient-centric AI proving useful in clinical workflows and interpreting X-rays holistically. With RayDINO and small task-specific adapters, we reach state-of-the-art results and improve generalization to unseen populations while mitigating bias, illustrating the true promise of foundation models: versatility and robustness.