We report the performance of a 10 atm Xenon/trimethylamine time projection chamber (TPC) for the detection of X-rays (30 keV) and γ-rays (0.511-1.275 MeV) in conjunction with the accurate tracking of the associated electrons. When operated at such a high pressure and in 1%-admixtures, trimethylamine (TMA) endows Xenon with an extremely low electron diffusion (1.3 ± 0.13 mm-σ (longitudinal), 0.8 ± 0.15 mm-σ (transverse) along 1 m drift) besides forming a convenient 'Penning-Fluorescent' mixture. The TPC, that houses 1.1 kg of gas in its fiducial volume, operated continuously for 100 live-days in charge amplification mode.The readout was performed through the recently introduced microbulk Micromegas technology and the AFTER chip, providing a 3D voxelization of 8mm×8mm×1.2mm for approximately 10 cm/MeV-long electron tracks. Energy resolutions at full width half maximum (FWHM) inside the fiducial volume ranged from 14.6%(30keV) to 4.6%(1.275MeV).This work was developed as part of the R&D program of the NEXT collaboration for future detector upgrades in the search of the neutrino-less double beta decay (ββ0ν) in 136 Xe, specifically those based on novel gas mixtures. Therefore we ultimately focus on the calorimetric and topological properties of the reconstructed MeV-electron tracks. In particular, the obtained energy resolution has been decomposed in its various contributions and improvements towards achieving the 1.4% 1MeV/ε levels obtained in small sensors are discussed.