jmc

Since $z^2=24-32i$, we must have $|z^2|=|24-32i|=|8(3-4i)|=8|3-4i|=8(5)=40$. We also have $|z{|}^2=|z|\cdot |z|=|(z)(z)|=|z^2|$, so $|z^2|=40$ means that $|z{|}^2=40$, which gives us $|z|=\sqrt{40}=\boxed{2\sqrt{10}}$.