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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+20x^68+18x^69+59x^70+48x^71+221x^72+44x^73+65x^74+16x^75+14x^76+2x^77+3x^78+1x^138

The gray image is a linear code over GF(2) with n=288, k=9 and d=136.
This code was found by Heurico 1.16 in 0.248 seconds.