The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+56x^69+108x^70+104x^71+59x^72+52x^73+60x^74+20x^75+20x^76+16x^77+4x^79+4x^80+2x^84+4x^85+2x^88

The gray image is a linear code over GF(2) with n=288, k=9 and d=138.
This code was found by Heurico 1.11 in 0.093 seconds.