A gaseous pixel readout module with four GridPix chips, called the quad, has been developed as a building block for a large time projection chamber readout plane. The quad module has dimensions 39.6mm×28.38mm and an active surface coverage of 68.9%. The GridPix chip consists of a Timepix3 chip with integrated amplification grid and have a high efficiency to detect single ionization electrons, which enable to make a precise track position measurement. A quad module was installed in a small time projection chamber and measurements of 2.5GeV electrons were performed at the ELSA accelerator in Bonn, where a silicon telescope was used to provide a reference track. The error on the track position measurement, both in the pixel plane and drift direction, is dominated by diffusion. The quad was designed to have minimum electrical field inhomogeneities and distortions, achieving systematics of better than 13µm in the pixel plane. The resolution of the setup is 41µm, where the total systematic error of the quad detector is 24µm.