  We prove that the Besicovitch Covering Property (BCP) does not hold for some
classes of homogeneous quasi-distances on Carnot groups of step 3 and higher.
As a special case we get that, in Carnot groups of step 3 and higher, BCP is
not satisfied for those homogeneous distances whose unit ball centered at the
origin coincides with a Euclidean ball centered at the origin. This result
comes in constrast with the case of the Heisenberg groups where such distances
satisfy BCP.
