Dephased $14\times 14$ orbits can be obtained from $F_2$ and dephased $7\times 7$ complex Hadamard matrices using the Diţă's method.
For example: $$\begin{aligned} FP_{14}^{(7)}(a,b,c,d,e,f,g) &= \left[\begin{array}{l|l} \big[F_2\big]_{1,1}\cdot F_7^{(0)} & \big[F_2\big]_{1,2}\cdot \mathbb{D}(b,c,d,e,f,g)\cdot P_7^{(1)}(a)\\ \hline \big[F_2\big]_{2,1}\cdot F_7^{(0)} & \big[F_2\big]_{2,2}\cdot \mathbb{D}(b,c,d,e,f,g)\cdot P_7^{(1)}(a)\\ \end{array}\right], \\ \\ \\ FC_{14\Sigma}^{(6)}(a,b,c,d,e,f) &= \left[\begin{array}{l|l} \big[F_2\big]_{1,1}\cdot F_7^{(0)} & \big[F_2\big]_{1,2}\cdot \mathbb{D}(a,b,c,d,e,f)\cdot C_{7\Sigma}^{(0)}\\ \hline \big[F_2\big]_{2,1}\cdot F_7^{(0)} & \big[F_2\big]_{2,2}\cdot \mathbb{D}(a,b,c,d,e,f)\cdot C_{7\Sigma}^{(0)}\\ \end{array}\right], \\ \\ \\ PP_{14}^{(8)}(a,b,c,d,e,f,g,h) &= \left[\begin{array}{l|l} \big[F_2\big]_{1,1}\cdot P_7^{(1)}(a) & \big[F_2\big]_{1,2}\cdot \mathbb{D}(c,d,e,f,g,h)\cdot P_7^{(1)}(b)\\ \hline \big[F_2\big]_{2,1}\cdot P_7^{(1)}(a) & \big[F_2\big]_{2,2}\cdot \mathbb{D}(c,d,e,f,g,h)\cdot P_7^{(1)}(b)\\ \end{array}\right], \\ \\ \\ PC_{14\Sigma}^{(7)}(a,b,c,d,e,f,g) &= \left[\begin{array}{l|l} \big[F_2\big]_{1,1}\cdot P_7^{(1)} & \big[F_2\big]_{1,2}\cdot \mathbb{D}(b,c,d,e,f,g)\cdot C_{7\Sigma}^{(0)}\\ \hline \big[F_2\big]_{2,1}\cdot P_7^{(1)} & \big[F_2\big]_{2,2}\cdot \mathbb{D}(b,c,d,e,f,g)\cdot C_{7\Sigma}^{(0)}\\ \end{array}\right], \\ \\ \\ CC_{14\Sigma_1\Sigma_2}^{(6)}(a,b,c,d,e,f) &= \left[\begin{array}{l|l} \big[F_2\big]_{1,1}\cdot C_{7\Sigma_1}^{(0)} & \big[F_2\big]_{1,2}\cdot \mathbb{D}(a,b,c,d,e,f)\cdot C_{7\Sigma_2}^{(0)}\\ \hline \big[F_2\big]_{2,1}\cdot C_{7\Sigma_1}^{(0)} & \big[F_2\big]_{2,2}\cdot \mathbb{D}(a,b,c,d,e,f)\cdot C_{7\Sigma_2}^{(0)}\\ \end{array}\right], \end{aligned}$$ where $\Sigma,\Sigma_1,\Sigma_2\in\{A,B,C,D\}$ and $\mathbb{D}(\varphi_1,\dots,\varphi_6) = {\rm diag}\big(1,i\varphi_1,\dots, i\varphi_6\big): \varphi_k\in[0,2\pi)$.