The design of a detector system comprised of four silicon sensors bumpbonded 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 ± 0.5) µm and (4.5 ± 0.3) µm for 100 µm and 300 µm thick sensors, respectively. The timestamps from the detectors are also measured with fine precision, yielding time resolutions of (452±10) ps, (420±10) ps, (639±10) ps, (631±10) ps for the two 100 µm and two 300 µm thick sensors respectively. These measurements are combined to a track time resolution of (340 ± 5) ps.