Let $$\gamma=\frac{1}{3} \sqrt{396+18\sqrt[3]{8468+12\sqrt{12309}}+3\sqrt[3]{1829088-2592\sqrt{12309}}}$$ and let $a_1$ and $a_2$ and their conjugate be the four roots of the polynomial $$ f(a) = 1008a^4-(336\gamma-1344)a^3-\left(\gamma^5-132\gamma^3-56\gamma^2+1088\gamma +1232\right)a^2-\left(336\gamma-1344\right)a+1008. $$ Eventually for $a=a_1$ or $a_2$ let $$b+c=-\frac{1}{48}\left( 30a^7+53a^6-83a^5-56a^4+117a^3-176a^2+103a+59 \right).$$ Then the circulant cores of two complex Hadamard matrices $Q_{11A}^{(0)}$ and $Q_{11B}^{(0)}$ are induced by the vector $x = \left[a,b,\bar{b},c,\bar{c},\bar{a},\bar{c},c,\bar{b},b\right]$ [37].