In this paper, we study quaternary quasi-cyclic (QC) codes with even length components. We determine the structure of one generator quaternary QC codes whose cyclic components have even length. By making use of their structure, we establish the size of these codes and give a lower bound for minimum distance. We present some examples of codes from this family whose Gray images have the same Hamming distances as the Hamming distances of the best known binary linear codes with the given parameters. In addition, we obtain a quaternary QC code that leads to a new binary non-linear code that has parameters (96, 2(26), 28).