In this paper we give three constructions of cyclic self-orthogonal codes over Z_2^k, for k>=3, from Boolean functions on n variables. The first construction for each k, 3<=k<=n, yields a self-orthogonal Z_2^k-code of length 2^{n+2} with all Euclidean weights divisible by 2^{k+1}. In the remaining two constructions, for each even n and k<= 3, we generate a self-orthogonal Z_2^k-code of length 2^{n+1}. All Euclidean weights in the constructed code are divisible by 2^{2k-1} or 2^{k+1}, depending on which of the two constructions is used.