A surface of degree $24$ with $1440$ singularities of type $D\mathrm{\_}4$

Using the invariant algebra of the reflection group denoted by $G\mathrm{\_}32$ in Shephard-Todd classification, we construct three irreducible surfaces in $P^3$ with many singularities: one of them has degree $24$ and contains $1440$ quotient singularities of type $D\mathrm{\_}4$.