A set of isolated complex Hadamard matrices found by V. Elser in 2011 (private communication).
Let $a$, $b$ and $c$ be unimodular numbers and $$\begin{aligned} V_{8\Sigma}&=\left[\begin{array}{rrrrrrrr} -1 & -1 & b & b & c & c & a & a \\ -1 & b & -1 & c & b & a & c & -a \\ b & -1 & c & -1 & a & b & -a & c \\ b & c & -1 & a & -1 & -a & b & -c \\ c & b & a & -1 & -a & -1 & -c & b \\ c & a & b & -a & -1 & -c & -1 & -b \\ a & c & -a & b & -c & -1 & -b & -1 \\ a & -a & c & -c & b & -b & -1 & 1 \\ \end{array}\right]\\ &\simeq \left[\begin{array}{rrrrrrrr} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & -b & -\bar{b} & c\bar{b} & b\bar{c} & a\bar{c} & c\bar{a} & -1 \\ 1 & -\bar{b} & -c\bar{b}^2 & \bar{b}^2 & -a\bar{b}\bar{c} & -\bar{c} & \bar{b} & -c\bar{a}\bar{b} \\ 1 & c\bar{b} & \bar{b}^2 & -a\bar{b}^2 & \bar{b}\bar{c} & a\bar{b}\bar{c} & -\bar{a} & c\bar{a}\bar{b} \\ 1 & b\bar{c} & -a\bar{b}\bar{c} & \bar{b}\bar{c} & a\bar{c}^2 & \bar{c}^2 & \bar{a} & -b\bar{a}\bar{c} \\ 1 & a\bar{c} & -\bar{c} & a\bar{b}\bar{c} & \bar{c}^2 & \bar{c} & \bar{a}\bar{c} & b\bar{a}\bar{c} \\ 1 & c\bar{a} & \bar{b} & -\bar{a} & \bar{a} & \bar{a}\bar{c} & b\bar{a}^2 & \bar{a}^2 \\ 1 & -1 & -c\bar{a}\bar{b} & c\bar{a}\bar{b} & -b\bar{a}\bar{c} & b\bar{a}\bar{c} & \bar{a}^2 & -\bar{a}^2 \\ \end{array}\right]. \end{aligned}$$
Unitarity conditions for $V_{8\Sigma}$ form a system of non-linear equations $$ \left\{\begin{aligned} -\frac{1}{b} - b + \frac{b}{c} + \frac{c}{b} + \frac{c}{a} + \frac{a}{c} & = 0 \\ -\frac{1}{b} - \frac{1}{c} - b + \frac{b}{a} - c - \frac{c}{a} + \frac{a}{b} - \frac{a}{c} & = 0 \\ \frac{1}{c} + \frac{1}{a} + \frac{b}{a} + c + a + \frac{a}{b} & = 0 \end{aligned}\right. $$ the solution of which reads: $$ \begin{array}{r|r|r|r|} \Sigma & a & b & c \\ \hline A & -0.65089101 \pm 0.75917118i & -0.77995684 \mp 0.62583330i & 0.61833872 \pm 0.78591171i \\ B & 0.97412724 \pm 0.22600024i & -0.61833872 \mp 0.78591171i & -0.19417040 \pm 0.98096781i \\ C & -0.97412724 \mp 0.22600024i & 0.03255228 \mp 0.99947003i & 0.77995684 \mp 0.62583330i \\ D & 0.65089101 \pm 0.75917118i & 0.19417040 \mp 0.98096781i & -0.03255228 \mp 0.99947003i \\ \end{array}. $$ Matrix elements can be calculated analytically, see [175].
There are also four Butson-type solutions $(a,b,c)=(\pm i, \mp\sqrt{i}, ab)$ with non-zero defect value, $d\Big(V_8(a,b,c)\Big)=5$.