The readout and data acquisition systems designed for a first prototype of liquid xenon position sensitive gamma ray detector for Positron Emission Tomography is described, The problem of measurement of the gamma ray energy in the gridless multiwire ionisation chamber is considered. A previously suggested drift time based correction algorithm, allowing correction of the amplitude spectra for the contribution of positive ions, is experimentally tested. First ionisation spectra, with an energy resolution of 15-17%, are presented. A pulse shape discrimination method for rejecting the induction cross-talk between the wires, improving energy resolution and allowing the unambiguous identification of Compton scattered events in the detector, is described.