A gaseous pixel detector has been developed based on four Timepix3 chips, called a quad, that can serve as a building block for e.g. a large Time Projection Chamber readout plane. The quad was designed to have minimum electrical field inhomogeneities and distortions, achieving a tracking precision in the pixel plane with systematics of better than 20 μm. Due to the high efficiency to detect the ionization electrons a precise measurement of the energy loss dE/dx can be performed. In this article we present details about the construction of the quad and the results from a recent test beam experiment performed at the ELSA electron beam in Bonn where a silicon telescope was used to provide accurate tracking to study the quad detector.