Let N be an ideal in the ring O of gaussian integers. We consider the action of the motivic Galois group on the motivic fundamental group of the elliptic curve with CM by the ring O, punctured at the N-torsion points, and relate it to the geometry of the Bianchi threefold obtained by taking the quotient of the hyperbolic space by a congruence subgroup of GL(2,O) determined by the ideal N.