  In their homonymous article, Sam Payne and Thomas Willwacher construct a
combinatorial graph complex to compute the weight 11 part of the compactly
supported cohomology of the moduli space of curves $\cM_{g,n}$ and compute
explicitly the cohomology of the introduced graph complexes in cases of
complexes of excess zero, one, two, and three. In this paper, we extend the
computation the cohomology to excess four graph complexes. Along the way, we
give more details on generators, the computation process, and the definition of
the graph complex.
