The generator matrix 1 0 1 1 1 0 1 1 X 1 1 X 1 1 0 1 1 0 1 1 1 1 X X 1 1 1 1 1 1 1 1 1 0 1 1 0 X+1 1 X X+1 1 X 1 1 0 X+1 1 0 X+1 1 X X 1 1 1 1 0 0 0 X 0 X X X 0 0 0 X 0 X 0 0 X 0 0 X 0 X 0 X X 0 X X X 0 0 X X 0 0 X X X X 0 0 0 0 0 0 X X X X 0 X 0 X 0 X 0 0 0 X X 0 X X 0 0 X 0 X X 0 0 X X 0 0 generates a code of length 33 over Z2[X]/(X^2) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+15x^32+32x^33+14x^34+2x^50 The gray image is a linear code over GF(2) with n=66, k=6 and d=32. As d=32 is an upper bound for linear (66,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6. This code was found by Heurico 1.16 in 0.00574 seconds.