The generator matrix 1 0 0 0 1 1 1 0 0 0 X 1 1 1 1 X 1 X 1 0 X 1 1 0 X 1 1 0 X X 1 0 1 0 1 0 0 X 1 X+1 1 1 1 0 0 X 1 X+1 X 0 1 1 1 1 X X 1 0 X+1 0 1 1 1 X+1 1 X+1 0 0 1 0 0 0 0 X 1 X+1 1 1 X+1 1 X+1 1 X 1 X 1 X+1 X+1 X X 0 1 X+1 0 X X+1 1 X+1 X 0 0 0 1 1 X+1 X X+1 1 X 1 X+1 X 0 1 X+1 1 X X X 0 X+1 0 0 1 X+1 1 X 1 X 0 1 0 generates a code of length 33 over Z2[X]/(X^2) who´s minimum homogenous weight is 30. Homogenous weight enumerator: w(x)=1x^0+88x^30+72x^32+32x^34+25x^36+18x^38+11x^40+4x^42+3x^44+2x^46 The gray image is a linear code over GF(2) with n=66, k=8 and d=30. As d=30 is an upper bound for linear (66,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 0.0872 seconds.