The generator matrix 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 X 1 1 X 1 1 X 1 1 X 1 1 X 1 1 X 1 1 X 1 1 X X X X X X X 0 0 X X 0 X X 0 X 0 0 X 0 1 1 0 1 1 0 X+1 1 0 1 X+1 1 0 1 0 X+1 1 0 X+1 1 0 1 1 X X+1 1 X 1 1 X X+1 1 X 1 1 X X+1 1 X 1 1 X X+1 1 X 1 1 0 0 0 0 0 X X 0 0 X X X 0 X X X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X 0 X X 0 X X 0 X X 0 X 0 X 0 0 X 0 0 X 0 0 X 0 0 0 0 0 X X X X X X 0 0 0 0 0 X X 0 0 0 0 X 0 0 0 0 X X X X X X X X 0 X 0 X 0 0 X 0 0 0 0 0 0 0 X X X X X X X X X X X X 0 0 0 0 0 0 0 0 X X X 0 X 0 X X 0 0 0 X X 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X X X X X 0 X X 0 X X 0 X X X X X X X X X X X X X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 0 0 0 0 X X 0 X X 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X 0 X 0 0 0 0 X X X X 0 X 0 X 0 0 X 0 X 0 X 0 X 0 X 0 X X 0 X 0 X 0 X 0 0 X 0 0 X X X 0 X 0 0 0 X X 0 0 generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+190x^64+64x^72+1x^128 The gray image is a linear code over GF(2) with n=132, k=8 and d=64. As d=64 is an upper bound for linear (132,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 0.047 seconds.