Summary: In 1966, T. J. Wagner [Inf. and Control 9, 94–99 (1966; Zbl 0269.94006)] used computational search methods to construct a \([23,14,5]\) code. This code has been examined with much interest since that time, in hopes of finding a geometric construction and possible code extensions. In this article, we give a simple geometric construction for Wagner’s code and consider extensions of this construction.