We obtain 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：我们获得了$\mathbb{Z}_4$上所有可能的Plotkin最优二重Lee重量射影码的参数及其权重分布。通过构造一个无限族的二重码，我们证明了具有这些参数及其权重分布的码的存在性。由Shi等人（《Des Codes Cryptogr.》**88**(3):1-13, 2020）先前构造的码可作为我们结果的一个特例。我们还证明了$\mathbb{Z}_4$上任何Plotkin最优二重Lee重量射影码的Gray像与Calderbank和Kantor（《Bull. Lond. Math. Soc.》**18**:97-122, 1986）定义的SU1型二元二重射影码具有相同的参数和权重分布。