Variance of the fourth power of a lognormal

Suppose $\ln X$ is standard normal. The variance of $X^4$ can be written as $e^a-e^b$ for positive integers $a,b$. What is $a+b$?

$48$. Write $X=e^Z$ with $Z$ standard normal and use the moment generating function $\mathbb{E}[e^{tZ}]=e^{t^2/2}$. Then the second moment of $X^4$ is $e^{64/2}=e^{32}$ and its mean is $e^{16/2}=e^{8}$, so the variance is $e^{32}-e^{16}$ and $a+b=48$.