The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 X 1 1 1 1 1 0 1 0 1 1 0 0 X X X X X 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 X X 1 X X X X X 0 X X X 0 0 0 1 1 0 X 1 1 X 1 1 1 0 X 1 1 1 1 0 1 0 1 1 X 0 1 0 1 0 0 X 1 X+1 1 0 1 X X+1 1 X 1 1 0 1 0 1 X 1 X+1 0 X X+1 1 0 1 0 X 1 1 1 0 1 X X+1 0 1 X X+1 X X+1 0 1 X X X X+1 0 0 0 1 1 X X X X X 0 1 0 0 0 1 1 1 1 X+1 X 1 1 0 1 1 X+1 0 X 1 X+1 1 0 X+1 X X+1 X 0 X 0 1 X+1 0 0 1 0 0 0 0 X 1 1 1 1 X+1 1 1 0 X X X+1 X+1 X X+1 X 1 X+1 X+1 X X 1 1 1 X+1 X 0 0 0 X X X X 0 0 0 1 X 1 1 X X+1 X+1 X+1 1 0 1 X+1 X+1 X 1 1 0 0 X X 1 1 0 X+1 1 1 X+1 X 0 X+1 X+1 0 X+1 X 0 1 X 1 X X 0 1 1 0 1 1 1 0 0 0 0 0 1 1 X+1 X X+1 X+1 0 X 1 X 1 X+1 1 X 1 1 X X+1 1 0 X 0 X+1 X 1 0 X+1 1 X X+1 1 X 1 X 1 0 X+1 0 X+1 X+1 X+1 X+1 0 0 1 X 0 0 X 1 X 0 X+1 1 0 X 1 1 1 1 X 0 X+1 0 X X X 1 X+1 X+1 X 0 0 X+1 X+1 X 1 0 0 1 1 0 X 1 0 X+1 1 X 0 generates a code of length 92 over Z2[X]/(X^2) who´s minimum homogenous weight is 90. Homogenous weight enumerator: w(x)=1x^0+118x^90+52x^92+56x^94+6x^96+16x^98+4x^100+2x^106+1x^128 The gray image is a linear code over GF(2) with n=184, k=8 and d=90. As d=90 is an upper bound for linear (184,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 4.79 seconds.