The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X 0 X 0 X 0 X 0 X X X X X X X X X X X X X X X X X 0 0 0 0 0 0 X X 0 0 0 X X 0 X X 0 X X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X 0 0 0 X X X X X X X X X 0 X 0 X 0 X 0 X X X X X X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X 0 0 0 X X 0 X X 0 X X 0 0 0 0 X 0 0 0 0 0 0 0 X X X X X X X X X 0 X X 0 0 X X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X 0 0 0 0 X X 0 0 0 X X 0 0 0 X X 0 X X 0 0 0 0 X 0 0 0 X X X X X 0 X X 0 0 0 0 0 0 0 0 0 X X X X 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X 0 0 0 0 0 0 0 0 X X X X 0 0 0 X X 0 0 0 0 0 X X X 0 0 X X X 0 0 0 0 0 0 X 0 X X X 0 0 0 0 X X X X 0 0 0 X X X X X X 0 0 X X 0 0 0 X X X X 0 0 0 0 0 0 X X X X 0 0 X X X X 0 0 0 0 X X X X 0 0 0 0 X X 0 0 0 0 X X X 0 0 0 0 X X 0 X 0 0 0 0 0 0 X X 0 X X 0 X X X 0 0 X 0 X X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 X X 0 0 0 X X X X 0 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 0 0 0 0 0 X X 0 X 0 X 0 X X generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+78x^80+96x^82+32x^86+48x^88+1x^160 The gray image is a linear code over GF(2) with n=166, k=8 and d=80. As d=80 is an upper bound for linear (166,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 0.164 seconds.