On the classification of the equitable partitions of the 12-cube with the quotient matrix [[0,12],[4,8]]

It is told about the results (j.w. with K.V.Vorob'ev) of computer-aimed classification of the equitable partitions the 12-cube with the quotient matrix [[0,12],[4,8]], or, equivalently, Boolean functions with a proportion 1/4 of ones achieving the bound on correlation immunity. It is established that there are exactly 16 equivalence classes of such functions; one coloring corresponds to a linear code of dimension 10, two colorings correspond to codes whose linear span coincides with the entire space (that is, codes of full rank, 12), the remaining 13 to codes of 'intermediate' rank 11. An approach is described that makes it possible to obtain the classification.