$H_8$

$${\rm LOG}\left(H_8\right)=\pi \left[\begin{array}{rrrrrrrr} \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\ \bullet & 1 & \bullet & 1 & \bullet & 1 & \bullet & 1\\ \bullet & \bullet & 1 & 1 & \bullet & \bullet & 1 & 1\\ \bullet & 1 & 1 & \bullet & \bullet & 1 & 1 & \bullet\\ \bullet & \bullet & \bullet & \bullet & 1 & 1 & 1 & 1\\ \bullet & 1 & \bullet & 1 & 1 & \bullet & 1 & \bullet\\ \bullet & \bullet & 1 & 1 & 1 & 1 & \bullet & \bullet\\ \bullet & 1 & 1 & \bullet & 1 & \bullet & \bullet & 1 \end{array}\right]$$

Note that $$H_8 = P_L\cdot D_8^{(4)}(0,0,0,0) \cdot P_R$$ for $$P_L=\left[\begin{array}{cccccccc} 1 &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet\\ \bullet &1 &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet\\ \bullet &\bullet &1 &\bullet &\bullet &\bullet &\bullet &\bullet\\ \bullet &\bullet &\bullet &\bullet &\bullet &\bullet &1 &\bullet\\ \bullet &\bullet &\bullet &\bullet &1 &\bullet &\bullet &\bullet\\ \bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &1\\ \bullet &\bullet &\bullet &1 &\bullet &\bullet &\bullet &\bullet\\ \bullet &\bullet &\bullet &\bullet &\bullet &1 &\bullet &\bullet\end{array}\right] \, \text{and} \quad P_R\left[\begin{array}{cccccccc} 1 &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet\\ \bullet &\bullet &\bullet &\bullet &1 &\bullet &\bullet &\bullet\\ \bullet &1 &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet\\ \bullet &\bullet &\bullet &\bullet &\bullet &\bullet &1 &\bullet\\ \bullet &\bullet &\bullet &1 &\bullet &\bullet &\bullet &\bullet\\ \bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &1\\ \bullet &\bullet &1 &\bullet &\bullet &\bullet &\bullet &\bullet\\ \bullet &\bullet &\bullet &\bullet &\bullet &1 &\bullet &\bullet\end{array}\right].$$