Abstract: We report the performance of a 10 atm Xenon/trimethylamine time projection chamber (TPC) for the detection of X-rays (30 keV) and gamma-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 similar to 1%-admixtures, trimethylamine (TMA) endows Xenon with an extremely low electron diffusion (1.3 +/- 0.13 mm-sigma (longitudinal), 0.95 +/- 0.20 mm-sigma (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 8 mm x 8 mm x 1.2 mm for approximately 10 cm/MeV-long electron tracks. Resolution in energy (epsilon) at full width half maximum (R) inside the fiducial volume ranged from R = 14.6% (30 keV) to R = 4.6% (1.275 MeV). 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 (beta beta 0 nu) in Xe-136, 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 R =1.4%root MeV/epsilon levels obtained in small sensors are discussed.