One of the most promising technologies to search for neutrinoless double beta decay (0nubb) is a high pressure xenon gas (HPXe) time projection chamber (TPC) with electroluminescent (EL) amplification. The key advantage of an HPXe-EL TPC is the capability to uniquely image the track of the two emitted electrons in a 0nubb event, together with high energy resolution. The current imaging performance is limited by the diffusion of the ionization electrons during drift. MELODIC describes a research program to reduce diffusion by adding molecular additives to the xenon gas to improve the imaging capability in an EL HPGXe TPC enhancing the sensitivity to the 0nubb decay, within the context of the NEXT collaboration. The project in being developed in two stages: 1) characterization of the molecular additive in a small detector at the University of Texas at Arlington (USA) (Outgoing Phase); 2) exploit the new gas mixture to perform the measurement of the topological signature in the DEMO++ TPC at the Instituto de Fisica Corpuscular (SPAIN) and at the underground Laboratorio Subterráneo de Canfranc.