Binary codes from graphs on triples

For a set @W of size n>=7 and @W^{^3^} the set of subsets of @W of size 3, we examine the ternary codes obtained from the adjacency matrix of each of the three graphs with vertex set @W^{^3^}, with adjacency defined by two vertices as 3-sets being adjacent if they have zero, one or two elements in common, respectively.