The Neutrino Experiment with a Xenon TPC (NEXT) searches for the neutrinoless double-beta decay of Xe-136 using high-pressure xenon gas TPCs with electroluminescent amplification. A scaled-up version of this technology with about 1 tonne of enriched xenon could reach sensitivity to the half-life of neutrinoless double-beta decay better than 1E27 years with less than 5 years of operation, improving the current limits by at least one order of magnitude. Such a detector, known as NEXT-HD, represents a first step on a compelling path towards sensitivity to the parameter space defined by the inverted ordering of neutrino masses, and beyond.