Multicore fibers are expected to be a game-changer in the coming decades thanks to their intrinsic properties, allowing a larger transmission bandwidth and a lower footprint in optical communications. In addition, multicore fibers have recently been explored for quantum communication, attesting to their uniqueness in transporting high-dimensional quantum states. However, investigations and experiments reported in literature have been carried out in research laboratories, typically making use of short fiber links in controlled environments. Thus, the possibility of using long-distance multicore fibers for quantum applications is still to be proven. We characterize here for the first time, to the best of our knowledge, in terms of phase stability, multiple strands of a four-core multicore fiber installed underground in the city of L’Aquila, with an overall fiber length up to about 25 km. In this preliminary study, we investigate the possibility of using such an infrastructure to implement quantum-enhanced schemes, such as high-dimensional quantum key distribution, quantum-based environmental sensors, and more, in general, quantum communication protocols.