I have the following language
$\qquad \{0^i 1^j 2^k \mid 0 \leq i \leq j \leq k\}$
I am trying to determine which Chomsky language class it fits into. I can see how it could be made using a context-sensitive grammar so I know it is atleast context-sensitive. It seems like it wouldn't be possible to make with a context-free grammar, but I'm having a problem proving that.
It seems to pass the fork-pumping lemma because if $uvwxy$ is all placed in the third part of any word (the section with all of the $2$s). It could pump the $v$ and $x$ as many times as you want and it would stay in the language. If I'm wrong could you tell me why, if I'm right, I still think this language is not context-free, so how could I prove that?