The generator matrix

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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+14x^69+92x^70+40x^71+93x^72+8x^73+2x^74+2x^77+1x^82+2x^88+1x^90

The gray image is a linear code over GF(2) with n=284, k=8 and d=138.
This code was found by Heurico 1.16 in 0.163 seconds.