Predicting next visit diagnosis using Electronic Health Records (EHR) is an essential task in healthcare, critical for devising proactive future plans for both healthcare providers and patients. Nonetheless, many preceding studies have not sufficiently addressed the heterogeneous and hierarchical characteristics inherent in EHR data, inevitably leading to sub-optimal performance. To this end, we propose NECHO, a novel medical code-centric multimodal contrastive EHR learning framework with hierarchical regularisation. First, we integrate multifaceted information encompassing medical codes, demographics, and clinical notes using a tailored network design and a pair of bimodal contrastive losses, all of which pivot around a medical codes representation. We also regularise modality-specific encoders using a parental level information in medical ontology to learn hierarchical structure of EHR data. A series of experiments on MIMIC-III data demonstrates effectiveness of our approach.