Let $$N=2^kn$$ N = 2 k n where n is odd and k a positive integer. We present a canonical form decomposition for every cyclic code over $${\mathbb {Z}}_4$$ Z 4 of length N, where each subcode is concatenated by a basic irreducible cyclic code over $${\mathbb {Z}}_4$$ Z 4 of length n as the inner code and a constacyclic code over a Galois extension ring of $${\mathbb {Z}}_4$$ Z 4 for length $$2^k$$ 2 k as the outer code. For the case of $$k=2$$ k = 2 , by determining their outer codes, we give a precise description for cyclic codes over $${\mathbb {Z}}_4$$ Z 4 , present dual codes and investigate self-duality for cyclic codes over $${\mathbb {Z}}_4$$ Z 4 of length 4n. Then we list all self-dual cyclic codes over $${\mathbb {Z}}_4$$ Z 4 of length 28 and 60, respectively.