Is Chinese Remainder Theorem relevant here?

\[\large{\begin{cases} Z &=& (q_{1})(1 - i) \\ Z &=& (q_{2})(1 - 2i) - i \\ Z &=& (q_{3})(1 - 4i) + 2 \\ Z &=& (q_{4})(3 - 2i) + 2i \\ \end{cases} } \]

Let \(Z\) be a Gaussian integer and \(q_{1}\), \(q_{2}\), \(q_{3}\), & \(q_{4}\) be the Gaussian integral quotients of the system above, what is the least value of \( | Z | ^{2}\)?

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