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

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+26x^68+32x^69+37x^70+320x^71+37x^72+32x^73+26x^74+1x^142

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 26 seconds.