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  X  1  1  1  1 X^2  1  1  1  X  1  1  1  1  0  1  1  1  X  0  0  1 X^2 X^2 X^2  X  1  1  1  0  1  X  0  1 X^2  1  1  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X  X  X  X X^2+X  X  0 X^2+X X^2  X X^2  X  0  X X^2 X^2+X  X  0 X^2+X X^2 X^2+X  0  0 X^2 X^2+X X^2 X^2+X  X  X  X X^2+X X^2+X X^2+X X^2+X X^2+X  X  X  0  X  0  X X^2+X X^2  X X^2 X^2  X  X  X  0  X X^2+X X^2  0 X^2+X X^2+X X^2 X^2  X  0 X^2  0
 0  0  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X  0  0  0 X^2 X^2 X^2+X  X X^2  0  0 X^2+X X^2 X^2  X X^2+X  0  X  X X^2+X  X X^2+X  0  X X^2+X X^2  X X^2  0  X  0  X  0 X^2 X^2+X  X X^2 X^2+X  0 X^2 X^2+X  0  X X^2 X^2  X  0  X X^2 X^2  X  X  0  X  X  X X^2+X  X  X  0
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  0  X  X X^2  X X^2 X^2+X  0 X^2+X  0 X^2  X X^2  X  X X^2  X  X  0  0 X^2  X X^2+X  0  0 X^2 X^2  0  X  X  0 X^2+X  0 X^2+X X^2 X^2+X  X  0  X  X X^2+X X^2+X X^2 X^2+X  X  0 X^2  X X^2  0  0 X^2 X^2+X  0 X^2 X^2+X  X  X X^2+X  0
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2 X^2  X X^2 X^2+X  X  X X^2 X^2 X^2+X  0 X^2+X  0 X^2+X X^2+X X^2+X  0 X^2+X  0  X  0 X^2  0 X^2+X  X X^2+X X^2 X^2  X X^2+X X^2 X^2+X X^2+X  0  0 X^2+X  X X^2+X  X X^2+X  X X^2 X^2+X X^2+X X^2 X^2  0  0 X^2+X X^2  0  X X^2  0  0  0 X^2+X X^2+X X^2  X 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+25x^64+64x^65+109x^66+126x^67+119x^68+176x^69+172x^70+174x^71+217x^72+190x^73+155x^74+146x^75+100x^76+48x^77+52x^78+46x^79+41x^80+24x^81+22x^82+16x^83+8x^84+8x^85+4x^87+2x^89+1x^90+1x^92+1x^114

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 0.492 seconds.