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).