The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  0  X  1  1  X  1  1  X  X  1  1 X^2+X  1  1  X  1  0 X^2+X  1  1 X^2+X X^2+X  1  1  X  1  1  X  1  1 X^2+X  1  1 X^2  1  1  X X^2+X  1  0  0  1  X  1 X^2+X  0  1  X  0  1  1 X^2  1  1  1  1  1 X^2+X X^2+X X^2+X  1  1  1
 0  1  0  0  1 X+1  1 X^2+X X^2+1  1  X X^2+1 X^2+X  1 X^2+X+1  0 X^2  1 X+1  X  1 X^2+X+1  0  1  1  1  1 X^2+X X^2+X  1  0  1  X  1  1  X X^2 X^2+X X^2+X+1 X^2+X X^2+X+1 X^2  1 X^2+X+1 X^2  1 X^2+X X^2+1  X  X X^2+1  1 X+1  1  1 X+1  1  0  X X^2+X  1  0 X^2+1 X^2  1 X+1  1  1 X^2+X X^2+1 X+1  0
 0  0  1  1  1  0  1  1 X^2+1 X^2+1  1  0 X^2  X  1  X  1 X^2+X X^2+X  1 X^2+X+1  0 X^2  0 X^2+X+1  1  X  1 X+1 X^2+1  1  1  0 X^2 X^2+X  X  1 X+1 X^2  1 X^2+1 X+1  X X^2+1 X+1  1  1 X^2  1  1 X^2+X+1 X^2+X+1 X^2+1 X^2+X+1 X^2+X+1 X^2  X  1 X^2+1  1 X^2+1  1 X^2+X+1  X X^2  X X^2 X^2  1 X^2+1 X+1  0
 0  0  0  X  0  0 X^2 X^2 X^2+X  X  X  X  X X^2+X X^2+X X^2  0  0  0 X^2  0  X  X X^2+X X^2 X^2+X X^2  X X^2  X X^2+X  0 X^2+X  X X^2  0  X  X X^2+X X^2  0 X^2+X X^2  X X^2 X^2 X^2+X X^2 X^2  0 X^2+X  X  X  0  X  0  X X^2+X  X X^2+X  0 X^2  X X^2 X^2+X X^2+X  0  0  0  X  X X^2
 0  0  0  0  X X^2  X X^2+X X^2 X^2 X^2+X X^2+X  X X^2+X X^2+X  X  X X^2+X X^2+X  0  0  0 X^2 X^2 X^2  X  0 X^2+X X^2+X  0  0 X^2 X^2+X  X X^2+X  0 X^2+X  0  0 X^2 X^2+X X^2  X X^2  X X^2+X  0  0 X^2  0  X X^2 X^2+X X^2  X X^2+X X^2+X X^2  X  X  0 X^2+X X^2 X^2 X^2+X X^2  0 X^2  X X^2+X X^2 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+100x^64+222x^65+389x^66+526x^67+603x^68+746x^69+647x^70+652x^71+706x^72+702x^73+680x^74+466x^75+461x^76+426x^77+298x^78+232x^79+130x^80+94x^81+63x^82+12x^83+8x^84+16x^85+3x^86+7x^88+2x^89

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 3.65 seconds.