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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+39x^64+60x^65+94x^66+88x^67+121x^68+228x^69+170x^70+148x^71+212x^72+214x^73+171x^74+144x^75+91x^76+62x^77+57x^78+20x^79+27x^80+38x^81+15x^82+16x^83+20x^84+6x^85+4x^86+1x^88+1x^118

The gray image is a linear code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 0.559 seconds.