A non-strictly pseudoconvex domain for which the squeezing function tends to one towards the boundary

In recent work by Zimmer it was proved that if $\mathrm{\Omega }\subset {\mathbb{C}}^n$ is a bounded convex domain with $C^{\mathrm{\infty }}$-smooth boundary, then $\mathrm{\Omega }$ is strictly pseudoconvex provided that the squeezing function approaches one as one approaches the boundary. We show that this result fails if $\mathrm{\Omega }$ is only assumed to be $C^2$-smooth.