Plane valuations at infinity are classified in five types. Valuations in one of them determine weight functions which take values on semigroups of $${\mathbb Z}^2$$ Z 2 . These semigroups are generated by $$\delta $$ δ -sequences in $${\mathbb Z}^2$$ Z 2 . We introduce simple $$\delta $$ δ -sequences in $${\mathbb Z}^2$$ Z 2 and study the evaluation codes of maximal length that they define. These codes are geometric and come from order domains. We give a bound on their minimum distance which improves the Andersen–Geil one. We also give coset bounds for the involved codes.