  A new Gray map which is both an isometry and a weight preserving map from
R=F_2+vF_2+v^2F_2 to (F_2)^3 is defined. A construction for quantum error
correcting codes from cyclic codes over finite ring R=F_2+vF_2+v^2F_2, v^3=v is
given. The parameters of quantum codes which are obtained from cyclic codes
over R are determined.
