How do I create a pushdown automata or context-free grammar for this language?

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I have a final exam tomorrow, and in preparation, and one of the practice problems is to create a pushdown automaton for this language. My professor has said that it IS context-free, but I can't seem to find a grammar or PDA for it. Can someone help me out?

$L=\{ 0^i1^{2i+2j}0^{i+j}|i, j \ge 1\}$

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So it turns out that this language is NOT context-free. There was a small mixup and the problem was written incorrectly on the lecture slides.