A complex Hadamard matrix found by K. Beauchamp and R. Nicoară [3]
$$B_9=B_9^{(0)}=\left[\begin{array}{rrrrrrrrr} 1& 1& 1& 1& 1& 1& 1& 1& 1\\ 1& -1&\varepsilon^3&\varepsilon^3& -1&\varepsilon^9&\varepsilon^8&\varepsilon^7& \varepsilon\\ 1&\varepsilon^4& -1&\varepsilon^7& \varepsilon&\varepsilon^3& -1&\varepsilon^9&\varepsilon^9\\ 1&\varepsilon^3&\varepsilon^7& -1& \varepsilon&\varepsilon^8&\varepsilon^9&\varepsilon^3& -1\\ 1&\varepsilon^9& \varepsilon& -1& -1&\varepsilon^3&\varepsilon^7&\varepsilon^2&\varepsilon^7\\ 1&\varepsilon^9& -1& \varepsilon&\varepsilon^3& -1& \varepsilon&\varepsilon^7&\varepsilon^6\\ 1& \varepsilon&\varepsilon^7&\varepsilon^9&\varepsilon^6& \varepsilon& -1& -1&\varepsilon^3\\ 1&\varepsilon^7&\varepsilon^9&\varepsilon^4&\varepsilon^9& -1&\varepsilon^3& -1& \varepsilon\\ 1& -1&\varepsilon^2&\varepsilon^9&\varepsilon^7&\varepsilon^7&\varepsilon^3& \varepsilon& -1 \end{array}\right]:\quad\varepsilon=\exp(2\pi i/10).$$The defect of $B_9$ is $2$ so it might be part of a family of non-equivalent Hadamard matrices.
update 2017/03/10
It is a part of a non-affine $2$-dimensional family, see $K_9^{(2)}$ [161], [166].