The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 X X X 0 X X 0 0 X X X X 1 1 1 1 1 1 1 1 0 1 0 0 X 1 X+1 1 0 1 X X+1 1 X X 1 X 1 0 0 X+1 X+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 X 1 X X+1 X+1 0 0 1 0 0 0 0 X 1 1 1 1 1 1 X X+1 X+1 X X X+1 X+1 X X+1 X+1 1 X 0 1 X 0 X+1 0 1 X 0 X 1 1 X X 0 1 1 X+1 X 0 0 0 1 1 X+1 X X+1 X+1 0 X 1 1 X+1 0 1 X+1 X 1 X 0 X+1 0 X X 0 1 X+1 0 X+1 1 1 X+1 X X X+1 1 0 1 X+1 X X X+1 1 X 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+86x^42+76x^44+44x^46+7x^48+20x^50+10x^52+4x^54+6x^58+2x^60 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 0.153 seconds.