The generator matrix 1 0 0 1 1 1 X 1 1 1 0 X 0 1 1 1 0 1 1 0 1 1 0 X 1 1 0 1 X X 0 X 1 0 1 1 1 0 X 1 1 1 X X X 0 1 0 0 1 X+1 1 0 1 X+1 1 1 0 0 X X+1 1 X X+1 1 X 1 1 1 X+1 1 1 0 1 0 1 1 X X X 0 X 1 1 1 X+1 1 0 1 1 0 0 1 1 1 0 1 X X+1 X X X+1 1 X+1 X X+1 X+1 0 1 1 1 X 0 X 0 0 X X+1 X 1 1 1 0 0 X+1 X 1 X+1 0 1 X+1 X 1 X 1 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X X X 0 X X 0 0 0 X 0 X X 0 X X 0 0 0 0 X 0 0 0 0 X X 0 X 0 0 X X X X X 0 0 0 X X 0 0 0 X X X X X 0 0 0 X 0 X X 0 X X 0 0 0 X 0 0 0 generates a code of length 45 over Z2[X]/(X^2) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+101x^42+48x^44+56x^46+5x^48+26x^50+8x^52+2x^56+9x^58 The gray image is a linear code over GF(2) with n=90, k=8 and d=42. As d=42 is an upper bound for linear (90,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 40 seconds.