jmc

We may carry out long division in base 4 just as in base 10. We have $$\begin{array}{cccccc}\text{multicolumn}2r& & & 3& 3& \\ \text{cline}3-61& 1& 1& 0& 2& 3\\ \text{multicolumn}2r& & 3& 3& \downarrow & \\ \text{cline}4-5\text{multicolumn}2r& & 0& 3& 3& \\ \text{multicolumn}2r& & & 3& 3& \\ \text{cline}5-6\text{multicolumn}2r& & & & 0& \end{array}$$for a quotient of $\boxed{33_4}$. Note that in the above calculation we have used that $11_4\cdot 3_4=5_{10}\cdot 3_{10}=15_{10}=33_4$. Then, for the second step we used $33_4$ divided by $11_4$ is $3_4$.