We will generalize a theorem given by R. M. Wilson about weights modulo p t in linear codes to a divisible code version, where by divisible codes, we mean linear codes over finite fields whose codewords all have weights divisible by some integer larger than 1. Employing a similar idea, we will give an upper bound on the dimension of a divisible code by some divisibility property of its weight enumerator modulo p e . We will then discuss some applications of the bound.