Context Free Grammar $L=\{a^ib^{2i}c^{2i} | i>1\}$
Your language is not context-free. You can see this by applying the inverse of the homomorphism which sends $a$ to $a$, $b$ to $bb$ and $c$ to $cc$; this results in the language $\{a^ib^ic^i : i &gt; 1\}$, which differs from a well-known non-context-free language by just a finite number of words.