Language of particular CFG Let:
$ G = &lt;V, \Sigma, R, S &gt;: \\
V = \{ S,A,B,C \} \\
\Sigma = \{0, 1\} \\
R: \\
S \to CSC|A \\
A \to 0B1|1B0 \\
B \to CB|\epsilon\\
C \to 1|0 
$

I need to find the language (no need to formally prove).
I have written many words but cannot seem to find a rule.
After trying that path I rewrote the grammar in a shorter rules:

$$
S \to 0S0|0S1|1S0|1S1|0B1|1B0 \\
B \to 1B|0B|\epsilon
$$

What should be my way of finding any pattern? to go each possible path independently ?
First, let us notice the following:
$$
L(S) = \{ xyz \mid x,z \in \{0,1\}^*, |x|=|z|, y \in L(A) \} \\
L(A) = 0L(B)1 \cup 1L(B)0 \\
L(B) = (0+1)^*
$$
Putting everything together, we get
$$
L(G) = \{ x\sigma y \tau z \mid x,y,z \in \Sigma^*, \sigma,\tau \in \Sigma, |x|=|z|, \sigma \neq \tau \}
$$
In other words, a word $w$ is in the language if there exists $i \leq |w|/2$ such that the $i$th symbol from the left is different from the $i$th symbol from the right. The condition $i \leq |w|/2$ can be eliminated, and we get that for some $i$, the $i$th symbol of $w$ is different from the $i$th symbol of $w^R$. In other words, $w \neq w^R$.

So your grammar generates the language of non-palindromes.