The generator matrix

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

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+124x^69+27x^70+16x^71+28x^72+24x^73+24x^77+4x^78+3x^80+4x^85+1x^86

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 51.6 seconds.