  We present the results of a lattice calculation of four-quark states with the
quark contents $\bar{b}\bar{c}q_1q_2$ where $q_1,q_2 \in u,d,s$. For the spin 1
states, when the light quark ($q_1, q_2$) masses are lighter, we find at least
one energy level below the possible elastic threshold energy levels. These
calculations are performed on three dynamical $N_f = 2+1+1$ highly improved
staggered quark ensembles at lattice spacings of about 0.12, 0.09, and 0.06 fm.
We use the overlap action for light to charm quarks while a non-relativistic
action with non-perturbatively improved coefficients is employed for the bottom
quark.
