Néron-Severi lattice $NS(S)$ contains the $ADE$ lattices that correspond to the types of the singular fibers. For example, that a K3 surface $S$ is $H\oplus E_7\oplus E_7$-lattice polarized means that the Néron-Severi lattice $NS(S)$ includes the lattice $ H\oplus E_7\oplus E_7$, and this is equivalent to the condition that the K3 surface $S$ is elliptically fibered with a section, the singular fibers of which include two type $III^*$ fibers (or worse). K3 surfaces with $H\oplus E_7\oplus E_7$ lattice polarization are parametrized by the bounded symmetric domain of type $IV$, $D_{2,4}$, modded out by the symmetry of the orthogonal complement of the lattice $ H\oplus E_7\oplus E_7$ inside the K3 lattice $\Lambda_{K3}$: $$\label{symmetry 2,4 in 2.1}
D_{2,4} / O^+(L^{2,4}).$$ $L^{2,4}$ denotes the orthogonal complement of $ H\oplus E_7\oplus E_7$ inside the K3 lattice $\Lambda_{K3}$. Because the K3 lattice $\Lambda_{K3}$ is isometric to $E_8^2\oplus H^3$, $L^{2,4}$ can also be defined as the orthogonal complement of $E_7\oplus E_7$ in the lattice $E_8^2\oplus H^2$.

By utilizing the F-theory/heterotic duality, eight-dimensional non-geometric heterotic strings with unbroken $\mathfrak{e}_7\mathfrak{e}_7$, the moduli space of which is equivalent to (\[symmetry 2,4 in 2.1\]) were constructed in [@CMSE7]. In this note, we study the points in the moduli of such 