HMMT 2015 A1

Let $Q$ be a polynomial

$$Q(x)=a_{0}+a_{1} x+\cdots+a_{n} x^{n}$$

where $a_{0}, \ldots, a_{n}$ are nonnegative integers. Given that $Q(1)=4$ and $Q(5)=152$, find $Q(6)$.