The performance of an electroluminescence (EL) Time Projection Chamber (TPC) with a multi avalanche photodiode (APD) readout was studied in pure xenon at 3.8 bar. Intercalibration and reconstruction methods were developed and applied to the data yielding energy resolutions as good as 5.3$±$0.1 \% FWHM for 59.5 keV gammas from $^{241}$Am. This result was reproduced with a Monte Carlo (MC) based on Geant4 and Penelope which predicted 5.2 \% FWHM for the used setup. Point resolutions of $≈ 0.5$ mm were obtained with a pitch of 15 mm between the APDs. These results show that multi-APD readout is a competitive technology for EL detectors filled with pure xenon. ; Comment: 27 pages, 23 figures, submitted to JINST, Rev. 18.12.2014