A four-dimensional periodic Costas array of order six

We give a bijection from $[2]\times[3]$ onto itself whose graph, extended periodically in four coordinates, has distinct nonzero ordered ordinary difference vectors in every $2\times3\times2\times3$ window. Its order is $6$, whereas the proposed minimum-order restriction of Rubio and Torres would require $4$. A short proof keeps the signs of the two binary-coordinate differences and reduces the other two differences modulo three.