CFG for $w\#x$ where $|w| = |x|$ and $w \neq x^R$
A word belongs to your language if it has one of the following forms:
$$
\Sigma^i 0 \Sigma^j \# \Sigma^j 1 \Sigma^i \\
\Sigma^i 1 \Sigma^j \# \Sigma^j 0 \Sigma^i
$$
Given this, you should be able to construct a context-free grammar for $L$.