The generator matrix

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

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+89x^64+210x^65+468x^66+430x^67+685x^68+614x^69+771x^70+598x^71+768x^72+624x^73+671x^74+490x^75+588x^76+338x^77+332x^78+182x^79+152x^80+60x^81+44x^82+24x^83+15x^84+8x^85+17x^86+4x^87+6x^88+2x^89+1x^90

The gray image is a linear code over GF(2) with n=288, k=13 and d=128.
This code was found by Heurico 1.16 in 3.7 seconds.