A new encoding scheme was developed that is applicable to bismuth germanate (BGO) detector units for a high resolution positron emission tomograph. The detector unit is composed of eight equal-size, 3 mm wide BGO crystals coupled to a dual-module square photomultiplier tube (PMT) through a pair of light guides. The light guides divide the scintillation light between the two modules of the PMT, with a ratio dependent on the crystal of origin. Mean detector pair spatial resolution as measured by the point spread function was 3.9 mm full width at half maximum (FWHM) and reconstructed image spatial resolution was 4.8 mm FWHM at the center of the field of view. Timing resolution between two detector units was 6.0 ns FWHM. Energy resolution was 24% FWHM for 511 keV gamma rays. The finest spots of the Derenzo phantom were clearly resolved.