  We refine our previous study of a $u d \bar{b} \bar{b}$ tetraquark resonance
with quantum numbers $I(J^{P})=0(1^{-})$, which is based on antiheavy-antiheavy
lattice QCD potentials, by including heavy quark spin effects via the mass
difference of the $B$ and the $B^{*}$ meson. This leads to a coupled channel
Schr\"odinger equation, where the two channels correspond to $BB$ and
$B^{*}B^{*}$, respectively. We search for $\mbox{T}$ matrix poles in the
complex energy plane, but do not find any indication for the existence of a
tetraquark resonance in this refined coupled channel approach. We also vary the
antiheavy-antiheavy potentials as well as the $b$ quark mass to further
understand the dynamics of this four-quark system.
