Is there a grammar for this language? $w^{m-1}aca^m$?
You attack it from the exact wrong side.
First, the language is the same as $\{w^m aca a^m|w\in\{a,b\},m\in\mathbb{N}\}$. For this, you apply a rule that adds $w$ on the left and $a$ on the right repeatedly, and then inserts $aca$ in the middle and is done. By using one rule that adds both on the left and the right side, you make the number of w's and a's the same.
$S \rightarrow WSa$
$S \rightarrow aca$
$W \rightarrow a|b$
That’s it.