Structured illumination is essential for high-performance ptychography. Especially in the extreme ultraviolet (EUV) range, where reflective optics are prevalent, the generation of structured beams is challenging and, so far, mostly amplitude-only masks have been used. In this study, we generate a highly structured beam using a phase-shifting diffuser optimized for 13.5 nm wavelength and apply this beam to EUV ptychography. This tailored illumination significantly enhances the quality and resolution of the ptychography reconstructions. In particular, when utilizing the full dynamics range of the detector, the resolution has been improved from 125 nm, when using an unstructured beam, to 34 nm. Further, ptychography enables the quantitative measurement of both the amplitude and phase of the EUV diffuser at 13.5 nm wavelength. This capability allows us to evaluate the influence of imperfections and contaminations on its "at wavelength" performance, paving the way for advanced EUV metrology applications and highlighting its importance for future developments in nanolithography and related fields.