Find the Undefined

$\large{z=\sqrt{-4} \left( \log _2 (-4) +\arcsin { \left( -4 \right) } \right)}$

If $Re(z)$ can be expressed in the form $\ln { (A-B\sqrt { C } )-D\pi }$ Where $A, B, C, D$ are natural numbers and C is not divisible by a perfect square, submit the value of $A+B+C+D$ as your answer.