In this paper, a recent bound on some Weil-type exponential sums over Galois rings is used in the construction of codes and sequences. The bound on these type of exponential sums provides a lower bound for the minimum distance of a family of codes over F-p, mostly nonlinear, of length p(m+1) and size p(2) (.) p(m)((D-[D/p2])), where 1 <= D <= p(m/2). Several families of pairwise cyclically distinct p-ary sequences of period p(p(m) - 1) of low correlation are also constructed. They compare favorably with certain known p-ary sequences of period p(m) - 1. Even in the case p = 2, one of these families is slightly larger than the family Q(D) of [H-K, Section 8.8], while they share the same period and the same bound for the maximum non-trivial correlation.