Let Z4denote the ring of integers modulo 4. The Galois ring GR(4,m), which consists of 4melements, represents the Galois extension of degreemover Z4. The constructions of codes over Z4have garnered significant interest in recent years. In this paper, building upon previous research, we utilize the defining-set approach to construct several classes of linear codes over Z4by effectively using the properties of the trace function from GR(4,m) to Z4. As a result, we have been able to obtain new infinite families of linear codes over Z4and completely determine their Lee weight distributions.