Reconstructed ptychographic X-ray computed tomography data set acquired at Diamond Light Source, instrument I13-1 (proposal MG24079-1) of the activated hierarchical porous sample Ni/Al${2}$O${3}$-ha. The data set is part of an artificial coking study of nickel based catalysts, which were investigated by ptychographic X-ray computed tomography. Detailed information regarding sample preparation and experimental conditions are available in the respective publication and electronic supplementary information.