MRI scans provide valuable medical information, however they also contain sensitive and personally identifiable information (PII) that needs to be protected. Whereas MRI metadata is easily sanitized, MRI image data is a privacy risk because it contains information to render highly-realistic 3D visualizations of a patient's head, enabling malicious actors to possibly identify the subject by cross-referencing a database. Data anonymization and de-identification is concerned with ensuring the privacy and confidentiality of individuals' personal information. Traditional MRI de-identification methods remove privacy-sensitive parts (e.g. eyes, nose etc.) from a given scan. This comes at the expense of introducing a domain shift that can throw off downstream analyses. Recently, a GAN-based approach was proposed to de-identify a patient's scan by remodeling it (e.g. changing the face) rather than by removing parts. In this work, we propose CP-MAE, a model that de-identifies the face using masked autoencoders and that outperforms all previous approaches in terms of downstream task performance as well as de-identification. With our method we are able to synthesize scans of resolution up to $256^3$ (previously 128 cubic) which constitutes an eight-fold increase in the number of voxels. Using our construction we were able to design a system that exhibits a highly robust training stage, making it easy to fit the network on novel data.