Suppose $z$ is a complex number with positive imaginary part, with real part greater than $1$, and with $|z| = 2$. In the complex plane, the four values $0$, $z$, $z^2$, and $z^3$ are the vertices of a quadrilateral with area $15$. What is the imaginary part of $z$?
(A) $\frac{3}{4}$ (B) $1$ (C) $\frac{4}{3}$ (D) $\frac{3}{2}$ (E) $\frac{5}{3}$