$\bar G=\frac{G}{\gamma_2G^p}$ is of class at most 2 when G is not powerful

Question

Let $G$ be finite p-group of class c and order $p^n$ that is not powerful then $\gamma_2\not\le G^p$ (second lower central series is not contained in $G^p$)
Let $\bar G=\frac{G}{\gamma_2G^p}$
How we can say $\bar G$ is a two-generator group of exponent p and class at most 2?