An Example on $s$-H-Convexity in ${\mathbb{C}}^2$

We construct a bounded domain $\mathrm{\Omega }$ in ${\mathbb{C}}^2$ with boundary of class ${\mathcal{C}}^{1,1}$, such that $\bar{\mathrm{\Omega }}$ has a Stein neighborhood basis, but is not $s$-H-convex for any real number $s\ge 1$.