  We analyze asymptotic symmetry algebras in (2+1)-dimensional non-AdS
higher-spin gravity with a focus on AdS$_2\times\mathbb{R}$ and
$\mathbb{H}_2\times\mathbb{R}$. We find a consistent set of boundary conditions
for spin-3 gravity in the non-principal embedding and calculate the
corresponding asymptotic symmetry algebra in the classical and quantum
mechanical case. In addition, we check for unitary representations of the
resulting quantum $\mathcal{W}_3^{(2)}$ algebra and give an interpretation of
the corresponding CFT.
