The design of a detector system comprised of four silicon sensors bump-bonded to Timepix4 ASICs is described together with its data acquisition system, operational infrastructure, and dedicated software. The spatial and temporal performance of the system are assessed with a 180 GeV/c mixed hadron beam at the CERN SPS and reported in detail. Particle tracks are reconstructed using time-space measurements from the four detector planes. The spatial hit resolution is assessed to be $(15.5\pm 0.5)$ $\mu$m and $(4.5\pm0.3)$ $\mu$m for 100 and 300 $\mu$m thick sensors, respectively. The timestamps from the detectors are also measured with fine precision, yielding time resolutions of $(452\pm10)$ ps, $(420\pm10)$ ps, $(639\pm10)$ ps, $(631\pm10)$ ps for the two 100 and two 300 $\mu$m thick sensors respectively. These measurements are combined to a track time resolution of $(340\pm 5)$ ps.
Comment: 15 pages, 15 images in 9 figures