In his paper [Some invariants for conics and their applications, Publ. RIMS (Kyoto Univ.) 19 (1983), 1139-1151] Naruki gives an example of a self-dual quartic surface in $\mathbb{P}^3$ with three singular points of type $A3$ and seven points of type $A1$ (i.e., ordinary double points).

The paper can be dowloaded here.

In his paper [Some invariants for conics and their applications, Publ. RIMS (Kyoto Univ.) 19 (1983), 1139-1151] Naruki gives an example of a self-dual quartic surface in $\mathbb{P}^3$ with three singular points of type $A_3$ and seven points of type $A_1$ (i.e., ordinary double points).

The paper can be dowloaded here.

In his paper [Some invariants for conics and their applications, Publ. RIMS (Kyoto Univ.) 19 (1983), 1139-1151] Naruki gives an example of a self-dual quartic surface in $\mathbb{P}^3$ with three singular points of type $A3$ and seven ordinary double points ($A1$).

The paper can be dowloaded here.

In his paper [Some invariants for conics and their applications, Publ. RIMS (Kyoto Univ.) 19 (1983), 1139-1151] Naruki gives an example of a self-dual quartic surface in $\mathbb{P}^3$ with three singular points of type $A3$ and seven points of type $A1$ (i.e., ordinary double points).

The paper can be dowloaded here.