The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  1 X^2 X^2+X X^2+X X^2  1  1 X^2+X  1  1 X^2+X  1  0  1  1  X  1 X^2  1  1  1  1  0  1  1  1  X X^2  1  0  X  1 X^2+X  X  X  X  0  1  1  1  1 X^2 X^2 X^2  0  0  1  1 X^2+X  0  1  X  1  1 X^2 X^2+X  1  1 X^2  1
 0  1  0 X^2 X^2+1  1  1  0  0 X^2 X^2+1  1  1  1 X^2+X  X  X X^2+X+1  1 X^2+X X+1  1  X  1 X^2+X+1  0  1 X^2+X  1 X+1 X^2+1  X X+1  1  X  0 X^2  X  1  1  1 X^2 X^2+X  1  1  1 X^2  1 X^2 X^2+X X^2  X  1  1  1  X  1 X^2+X+1 X^2+X  1 X^2  0  1  X  0  1 X^2  0 X^2+X  X X^2+X
 0  0  1 X^2+X+1 X+1 X^2 X^2+1  X  1  1 X^2+1 X^2+X  X X+1  1  1  X  1  X X^2 X+1 X^2  1 X^2+X+1  X X^2+1 X^2+X+1 X+1  1 X^2+X  0 X^2+X+1 X^2 X^2+1 X^2+1 X^2+X+1 X^2  1 X^2  X X^2+X  1 X^2+X X^2+1 X^2+X  0  X X+1 X^2+X  0  0  0 X^2+X+1  0 X+1 X^2+X  X X^2 X^2+1  0  1 X^2+X X+1 X^2+X  1 X^2+1  1 X+1 X^2+X+1  1  X

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+54x^68+142x^69+63x^70+72x^71+66x^72+38x^73+13x^74+16x^75+12x^76+12x^77+12x^78+4x^79+1x^80+4x^81+1x^84+1x^96

The gray image is a linear code over GF(2) with n=284, k=9 and d=136.
This code was found by Heurico 1.16 in 0.118 seconds.