The generator matrix 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 X 1 X 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 X X 0 X X 0 1 1 0 1 1 0 X+1 1 0 1 X+1 X+1 1 X+1 1 X+1 X+1 X 1 1 X 1 0 1 X+1 X+1 0 1 0 0 X+1 X X 1 1 X X 1 0 0 1 X+1 X+1 X+1 0 1 X X 1 1 0 0 X 0 0 0 0 0 0 0 0 X X X 0 0 X X 0 X 0 0 0 X X 0 0 X 0 X X X 0 0 0 X X X X 0 X X 0 0 X X X 0 0 X X 0 0 0 X 0 0 0 0 X X X 0 X X X X X 0 X 0 X X X 0 0 0 X 0 X 0 X 0 0 X 0 X 0 0 0 X X 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X 0 0 X 0 0 0 0 X X X X 0 X 0 X 0 0 0 0 0 X X 0 X X 0 X 0 X X 0 X 0 0 X X X 0 0 0 X X X X 0 X 0 0 0 0 0 X X X X X 0 X X 0 0 X 0 0 0 X 0 X X X X 0 X 0 0 0 0 X X 0 X 0 X 0 X 0 X X 0 0 0 0 X 0 X X 0 generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 48. Homogenous weight enumerator: w(x)=1x^0+119x^48+92x^52+33x^56+4x^60+4x^64+3x^72 The gray image is a linear code over GF(2) with n=102, k=8 and d=48. As d=48 is an upper bound for linear (102,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8. This code was found by Heurico 1.16 in 26.5 seconds.