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We refine our previous study of a udb¯b¯ tetraquark resonance with quantum numbers I(JP)=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 Schrödinger equation, where the two channels correspond to BB and B∗B∗, respectively. We search for 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.