Recently, several biophysical models and signal representations have been proposed for microstructure imaging based on tensor-valued, or multidimensional, diffusion MRI. The acquisition of the necessary data requires non-conventional pulse sequences, and data is therefore not available to the wider diffusion MRI community. To facilitate exploration and development of analysis techniques based on tensor-valued diffusion encoding, we share a comprehensive data set acquired in a healthy human brain. The data encompasses diffusion weighted images using linear, planar and spherical diffusion tensor encoding at multiple b-values and diffusion encoding directions. We also supply data acquired in several phantoms that may support validation. The data is hosted by GitHub: https://github.com/filip-szczepankiewicz/Szczepankiewicz_DIB_2019.