Fourth moment of gamma sum

Let $X_1 \sim \mathrm{Gamma}(1, 4), X_2 \sim \mathrm{Gamma}(2, 2)$ and $X_3 \sim \mathrm{Gamma}(3, 4)$ be three independent random variables. If $Y = X_1+2X_2+X_3$, then $E\left(\left(\frac{Y}{4}\right)^4\right)$ equals __________