Let $\bar { z }$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of
$$( \bar { z } ) ^ { 2 } + \frac { 1 } { z ^ { 2 } }$$
are integers, then which of the following is/are possible value(s) of $| z |$ ?
(A) $\left( \frac { 43 + 3 \sqrt { 205 } } { 2 } \right) ^ { \frac { 1 } { 4 } }$\\
(B) $\left( \frac { 7 + \sqrt { 33 } } { 4 } \right) ^ { \frac { 1 } { 4 } }$\\
(C) $\left( \frac { 9 + \sqrt { 65 } } { 4 } \right) ^ { \frac { 1 } { 4 } }$\\
(D) $\left( \frac { 7 + \sqrt { 13 } } { 6 } \right) ^ { \frac { 1 } { 4 } }$