What is the distribution of $\sqrt{X^2+Y^2}$ when $X$ and $Y$ are Gaussian but correlated?

Question

If $Z = \sqrt{X^2+Y^2}$, and $X$ and $Y$ are zero-mean i.i.d. normally-distributed random variables, then $Z$ is Rayleigh distributed.

What is the distribution of $Z$ if $X$ and $Y$ are correlated (but still zero-mean, normally-distributed random variables)?

Can't seem to find info on this scenario, even though it should be relatively common.