Let A be a finite set of at least two elements and let \(A^*\) denote the free monoid generated by A. A subset C of \(A^*\) is a code if the submonoid of \(A^*\) that it generates is free. A code of \(A^*\) is maximal if it is not properly contained in any other code of \(A^*\). The author gives a method for embedding a finitely generated free monoid as a dense subset of the unit interval. This gives an order topology for the monoid such that the submonoids generated by an important class of maximal codes occur as ``thick'' subsets (defined in an appropriate topological or measure theoretical sense). In particular he shows that a thin code is maximal if and only if the submonoid that it generates is dense on some interval. (A subset of \(A^*\) is called thin if it fails to meet every two sided ideal of \(A^*\).)