Remote monitoring of cardiovascular diseases plays an essential role in early detection of abnormal cardiac function, enabling timely intervention, improved preventive care, and personalized patient treatment. Abnormalities in the heart sounds can be detected automatically via computer-assisted decision support systems, and used as the first-line screening tool for detection of cardiovascular problems, or for monitoring the effects of treatments and interventions. We propose in this paper CardioPHON, an integrated heart sound quality assessment and classification tool that can be used for screening of abnormal cardiac function from phonocardiogram recordings. The model is pretrained in a self-supervised fashion on a collection of six small- and mid-sized heart sound datasets, enables automatic removal of low quality recordings to ensure that subtle sounds of heart abnormalities are not misdiagnosed, and provides a state-of-the-art performance for the heart sound classification task. The multimodal model that combines audio and socio-demographic features demonstrated superior performance, achieving the best ranking on the official leaderboard of the 2022 George B. Moody PhysioNet heart sound challenge, whereas the unimodal model, that is based only on phonocardiogram recordings, holds the first position among the unimodal approaches (a total rank 4), surpassing the models utilizing multiple modalities. CardioPHON is the first publicly released pretrained model in the domain of heart sound recordings, facilitating the development of data-efficient artificial intelligence models that can generalize to various downstream tasks in cardiovascular diagnostics.