On a -ultrahomogeneous oriented graph

The notion of a C -ultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and then a strongly connected C → 4 -ultrahomogeneous oriented graph on 168 vertices and 126 pairwise arc-disjoint 4-cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3, by altering a definition of the Coxeter graph via pencils of ordered lines of the Fano plane in which pencils are replaced by ordered pencils.