This dataset contains code and data to produce a list of all 192 centralising monoids on the set \(\{0,1,2\}\), including a witness for each of them. This gives a computational verification of the classification of centralising monoids published by Machida and Rosenberg in 2012 and 2013. Furthermore, some of the cpp-files and the context files form supplements to the bachelor dissertation of the second-named author. The code and the computed data contained in this upload also supplement the conference article that appeared in ICFCA 2023. A detailed description of the files in the dataset can be obtained from the file cent_mons3_witn.pdf (the code source for this file is given in cent_mons3_witn.tex).