For a complex number$z,$ let $Re\left(z\right)$ denote the real part of$z.$ Let S be the set of all complex numbers $z$satisfying $z^4–|z{|}^4=4i{z}^2,$ where  $i=\sqrt{-1}$. Then the minimum possible value of $|z_1–z_2{|}^2$, where      $z_1, z_{2 }\in S$with$Re( z_1 ) > 0$and $Re( z_2 )<0,$is ______