  In this article we consider solvable hypersurfaces of the form $N \exp(\R H)$
with induced metrics in the symmetric space $M = SL(3,\C)/SU(3)$, where $H$ a
suitable unit length vector in the subgroup $A$ of the Iwasawa decomposition
$SL(3,\C) = NAK$. Since $M$ is rank $2$, $A$ is $2$-dimensional and we can
parametrize these hypersurfaces via an angle $\alpha \in [0,\pi/2]$ determining
the direction of $H$. We show that one of the hypersurfaces (corresponding to
$\alpha = 0$) is minimally embedded and isometric to the non-symmetric
$7$-dimensional Damek-Ricci space. We also provide an explicit formula for the
Ricci curvature of these hypersurfaces and show that all hypersurfaces for
$\alpha \in (0,\frac{\pi}{2}]$ admit planes of both negative and positive
sectional curvature. Moreover, the symmetric space $M$ admits a minimal
foliation with all leaves isometric to the non-symmetric $7$-dimensional
Damek-Ricci space.
