The generator matrix 1 0 1 0 1 0 1 1 1 1 1 0 0 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 X X 1 1 X 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 X 1 1 X 1 1 X 1 1 X 1 1 0 1 1 0 1 1 X 1 1 X 1 1 0 1 1 0 0 1 0 1 0 1 X+1 X+1 X+1 0 X+1 1 1 1 0 X+1 1 0 X+1 1 0 X+1 1 0 X+1 1 X 1 1 X 1 1 X 1 1 X 1 1 1 1 X 1 1 X 1 X 1 X 1 0 X+1 0 X+1 1 0 X+1 1 0 X+1 1 X 1 1 X 1 1 X 1 1 X 1 1 0 X+1 1 0 X+1 1 X 1 1 X 1 1 0 X+1 1 X 1 1 0 0 X 0 0 0 0 0 X X X 0 X X 0 0 0 0 0 X X X X X X X X X X X X X 0 0 X 0 0 0 0 0 X X 0 X X 0 0 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 0 X X X X X X 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X X X 0 X 0 0 0 0 X 0 0 X 0 0 X 0 0 X 0 0 X 0 0 X 0 0 X 0 0 X 0 0 0 0 X 0 0 X 0 X 0 X X 0 X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X X 0 X 0 0 0 0 X 0 X 0 0 X X X X 0 0 X X X 0 X X 0 0 0 X 0 0 X X 0 X 0 X 0 X X 0 X X 0 X 0 0 X 0 0 X 0 X X 0 X 0 0 0 X X 0 X X 0 X X 0 X X X 0 0 X 0 0 0 X X X 0 0 X 0 0 0 X X 0 X 0 0 X 0 0 0 0 0 0 X X X X 0 X X X X X 0 0 X 0 0 X 0 0 X 0 0 0 0 0 X X X 0 0 X X X 0 X X X X 0 0 0 X X 0 0 0 0 X X X 0 0 X X X 0 X X 0 0 0 X X X 0 0 0 X X X X X X X X X X X X X 0 0 0 0 0 0 generates a code of length 90 over Z2[X]/(X^2) who�s minimum homogenous weight is 88. Homogenous weight enumerator: w(x)=1x^0+77x^88+128x^90+32x^92+15x^96+3x^120 The gray image is a linear code over GF(2) with n=180, k=8 and d=88. As d=88 is an upper bound for linear (180,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 19.9 seconds.