In this correspondence, a method of constructing optimal zero correlation zone (ZCZ) sequence sets over the 16-QAM+ constellation is presented. Based on 16-QAM orthogonal matrices and perfect ternary sequences, 16-QAM+ ZCZ sequence sets are obtained. The resulting ZCZ sequence sets are optimal with respect to the Tang-Fan-Matsufuji bound. Moreover, methods for transforming binary or quaternary orthogonal matrices into 16-QAM orthogonal matrices are proposed. The proposed 16-QAM+ ZCZ sequence sets can be potentially applied to communication systems using a 16-QAM constellation to remove the multiple access interference (MAI) and multi-path interference (MPI).