Why is $M_{21}\cong PSL_3(\mathbb{F}_4)$?

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I have recently been reading about the Large Mathieu Groups in "The Finite Simple Groups" by Robert Wilson and I have not come across any explanation of this isomorphism as of yet. In this context, $M_{21}$ is described as the point stabiliser of $M_{22}$, which is described as the point stabiliser of $M_{23}$, and so on.