The generator matrix 1 0 0 1 1 1 X 1 1 1 X 0 1 1 1 X 0 1 1 0 0 0 1 0 0 1 X+1 1 0 X 1 1 1 1 X X 0 1 X 0 1 0 0 0 1 1 1 0 1 X 1 X+1 1 X 1 0 0 1 1 1 0 X 1 0 0 0 X 0 0 0 0 0 X X 0 X X X 0 X 0 X X 0 0 0 0 0 X X 0 X 0 0 0 X X X 0 X 0 X 0 0 X generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 18. Homogenous weight enumerator: w(x)=1x^0+76x^18+69x^20+54x^22+23x^24+24x^26+3x^28+6x^30 The gray image is a linear code over GF(2) with n=42, k=8 and d=18. As d=18 is an upper bound for linear (42,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 0.674 seconds.