It is known that the number \(b(n)\) of inequivalent binary codes of length \(n\) gives the number of nonisomorphic binary \(n\)-matroids. The paper provides the asymptotic value of the number \(b(n)\) as \(n\to\infty\). Asymptotically, \(b(n)\equiv G(n)/n!\), where \(G(n)\) is the number of linear subspaces of \(\text{GF}(2)^n\).