Quadripartite version of the Hajnal–Szemerédi theorem

Let G be a quadripartite graph with N   vertices in each vertex class and each vertex is adjacent to at least (34)N vertices in each of the other classes. There exists an N0N0 such that, if N⩾N0N⩾N0, then G contains a subgraph that consists of N   vertex-disjoint copies of K4K4.