Context Free Grammar $L=\{a^ib^{2i}c^{2i} | i>1\}$

In one of my exams I needed to find a CFG for $ L=\{a^ib^{2i}c^{2i} | i>1\}$ .

however, it really seemed to me that it is not a CFG. I tried to show it is not using the pumping lemma, and think I managed, but I don’t really know if I did something wrong there.

So was I wrong or the question is wrong?

Thank you.