What is the smallest possible $\delta$-invariant of a non-planar Gorenstein curve singularity? I think the complete intersection $k[[x,y,z]]/(xy=z^2, zx=y^2))$ has $\delta$-invariant equal to $4$. Is $2$ or $3$ possible?

For the sake of concreteness, let's say that a curve singularity is a $1$-dimensional quotient of $k[[x_1, \dots, x_n]]$.