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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+136x^70+18x^72+72x^74+8x^76+12x^78+5x^80+4x^86

The gray image is a linear code over GF(2) with n=288, k=8 and d=140.
This code was found by Heurico 1.16 in 1.71 seconds.