Phase contrast X-ray imaging (PCXI) is an emerging imaging modality that has the potential to greatly improve radiography for medical imaging and materials analysis. PCXI makes it possible to visualise soft-tissue structures that are otherwise unresolved with conventional CT by rendering phase gradients in the X-ray wavefield visible. This can improve the contrast resolution of soft tissues structures, like the lungs and brain, by orders of magnitude. Phase retrieval suppresses noise, revealing weakly-attenuating soft tissue structures, however it does not remove the artefacts from the highly attenuating bone of the skull and from imperfections in the imaging system that can obscure those structures. The primary causes of these artefacts are investigated and a simple method to visualise the features they obstruct is proposed, which can easily be implemented for preclinical animal studies. We show that phase contrast X-ray CT (PCXI-CT) can resolve the soft tissues of the brain in situ without a need for contrast agents at a dose ~400 times lower than would be required by standard absorption contrast CT. We generalise a well-known phase retrieval algorithm for multiple-material samples specifically for CT, validate its use for brain CT, and demonstrate its high stability in the presence of noise.