  We study symbolic dynamical representations of actions of the first
Grigorchuk group $G$, namely its action on the boundary of the infinite rooted
binary tree, its representation in the topological full group of a minimal
substitutive $\mathbb{Z}$-shift, and its representation as a minimal system of
Schreier graphs. We show that the first system admits an SFT cover, and the
latter two systems are conjugate to sofic subshifts on $G$, but are not of
finite type.
