The only maximal affine Hadamard family stemming from $F_9$ is the $4$-parameter (self-cognate) orbit $$F_9^{(4)}(a,b,c,d)=F_9\circ{\rm EXP}\left(i R_{F_9^{(4)}}(a,b,c,d)\right)$$ where $$F_9=\left[\begin{array}{lllllllll} 1& 1& 1& 1& 1& 1& 1& 1& 1\\ 1& w&w^2&w^3&w^4&w^5&w^6&w^7&w^8\\ 1&w^2&w^4&w^6&w^8& w&w^3&w^5&w^7\\ 1&w^3&w^6& 1&w^3&w^6& 1&w^3&w^6\\ 1&w^4&w^8&w^3&w^7&w^2&w^6& w&w^5\\ 1&w^5& w&w^6&w^2&w^7&w^3&w^8&w^4\\ 1&w^6&w^3& 1&w^6&w^3& 1&w^6&w^3\\ 1&w^7&w^5&w^3& w&w^8&w^6&w^4&w^2\\ 1&w^8&w^7&w^6&w^5&w^4&w^3&w^2& w\end{array}\right]:\quad w=\exp(2\pi i/9)$$ and $$R_{F_9^{(4)}}(a,b,c,d)=\left[\begin{array}{ccccccccc} \bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet\\ \bullet&a&b&\bullet&a&b&\bullet&a&b\\ \bullet&c&d&\bullet&c&d&\bullet&c&d\\ \bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet\\ \bullet&a&b&\bullet&a&b&\bullet&a&b\\ \bullet&c&d&\bullet&c&d&\bullet&c&d\\ \bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet&\bullet\\ \bullet&a&b&\bullet&a&b&\bullet&a&b\\ \bullet&c&d&\bullet&c&d&\bullet&c&d\end{array}\right].$$