Let L CFL. Prove or disprove $B(L) = \{w : w \in L, |w|>10 \} $ is CFL

Question

I'm struggling with proving or disproving this question.
I didn't find any counterexamples, so I tend to think that I need to prove it.

$L$ is $CFL$, so exist $CFG$, $G=(V,Σ,R,S)$ that accepts $L$.
From here I'm not sure how should I build $B(L)$ (if proving is the correct answer).

Some suggestions would be nice.

Thanks.