X-ray phase contrast imaging (PCI) has shown great potential for clinical investigation of soft tissues. However, most of the existing X-ray PCI modalities require either a partially coherent source such as a synchrotron or complex setups that are barely compatible with low-dose and patient tomography. This work demonstrates the possibility to efficiently achieve PCI on a low coherence system with a conventional X-ray tube and a detector compatible with a clinical routine. This was accomplished by adapting the speckle-based imaging setup and the numerical phase retrieval processing methods to the low coherence and the low resolution of the experiment.