Computing a sextic twist
The correct answer depends on the way the towering is done (if any towering was done). I used the following towering:

$\mathbb{F}_{p^{2}}/(i^2+1)$

$\mathbb{F}_{p^{6}}/(y^3+\xi)$ with $\xi \in \mathbb{F}_{p^{2}}$

$\mathbb{F}_{p^{12}}/(x^2+\xi)$ with $\xi \in \mathbb{F}_{p^{2}}$

For this towering, $\mu^2=y$ and $\mu^3=x$.