The use of spreading codes with a zero correlation zone or a low correlation zone can reduce multiple access interference in code-division multiple-access (CDMA) radio systems. However, problems can arise from the limited number of codewords. In this paper it is shown that this shortage of codewords can be mitigated by a combination of two approaches. Existing constructions of binary and ternary codes for quasisynchronous CDMA are modified to double the number of spreading codewords. Increases in correlation are restricted to certain codeword pairs. A metaheuristic algorithm inspired by those used in frequency assignment is then used to assign these codewords. This is done in such a way that a satisfactory signal-to-interference ratio across the network is obtained. Excellent results are reported for several networks. Interference is lower than when a Gold code is used as a scrambling code. Bit-error-rate improvements are quantified in the case that binary phase shift keying is used.