We obtained all possible parameters of Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4,$ together with their weight distributions. We show the existence of codes with these parameters as well as their weight distributions by constructing an infinite family of two-weight codes. Previously known codes constructed by Shi et al. (\emph{Des Codes Cryptogr.} {\bf 88}(3):1-13, 2020) can be derived as a special case of our results. We also prove that the Gray image of any Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4$ has the same parameters and weight distribution as some two-weight binary projective codes of type SU1 in the sense of Calderbank and Kantor (\emph{Bull. Lond. Math. Soc.} {\bf 18}:97-122, 1986).

翻译：我们通过建立一个由两重代码组成的无限大家庭,显示了这些参数及其重量分布的代码的存在。以前由Shi等人建造的已知代码(\ emph{Des Codes cryptogr.}}\bf 88}(3):1-13,2020)可以作为我们结果的一个特例。我们还证明,任何位于$\mathbbb4$的普罗金-最优双利加权投影代码的灰色图像具有与卡尔德班和康托尔意义上的SU1型(\emph{Bull. Lod. Math. Soc.} {bf 18}:97-122,1986)的两重二重二重投影代码相同的参数和重量分布。