Maximum height is achieved when the projection is along the vertical direction,

$H_{max}=\frac{v^2}{2 g}=136 \mathrm{m}$

Now, for maximum range, angle of projection should be $45°$. Therefore,

$$\begin{gathered} R_{max}=\frac{v^2}{ g} \\ =2H_{max} \end{gathered}$$

$=2\left(136\right)$

$=272 \mathrm{m}$