Take $\mathcal{X}$ to be defined by the equation $tf_{4}+z_{0}z_{1}z_{2}z_{3}=0$ in $\mathbb{P}^{3}\times D$, where $D$ is a disk with coordinate $t$ and $f_{4}$ is a general homogeneous quartic polynomial on $\mathbb{P}^{3}$. It is easy to see that $\mathcal{X}$ is singular at the locus

$$\{t=f_{4}=0\}\cap Sing(\mathcal{X}_{0}).$$

As $\mathcal{X}_{0}$ is the coordinate tetrahedron, the singular locus of $\mathcal{X}_{0}$ consists of the six coordinate lines of $\mathbb{P}^{3}$, and $\mathcal{X}$ has four singular points along each such line, for a total of 24 singular points. Take $Z=Sing(\mathcal{X})$. Then away from $Z$, the projection $\mathcal{X}\rightarrow D$ is normal crossings, which yields condition (4) of the definition of toric degeneration. It is easy to see all other conditions are satisfied.