The generator matrix

 1  0  0  0  1  1  1  1 X^3  1 X^3+X X^2+X X^3+X^2+X  1  1  0  1  1  1  1 X^3+X^2  1  1 X^3+X^2  1 X^2+X  1 X^3+X^2+X X^2+X  1 X^2 X^3 X^3  1  1 X^2  0  1 X^3+X^2+X  1  1  1 X^3+X^2+X  1 X^3+X^2+X  1  1 X^3+X^2  1 X^3  1  1 X^2+X  0  1 X^3+X^2 X^3  X X^2  1  1  1  1 X^3+X X^3+X^2+X  X  1  1  1  0  1  1
 0  1  0  0  X X^2+1 X^3+X^2+X X^3+X^2+1  1 X^2+1  1  1 X^3+X X^3+X^2  1 X^2+X X^3+X^2+X+1  X  0 X^3+X+1  1 X^2+X+1  0 X^3+X^2 X^3+1 X^2+X X^3  1  1 X^2+X  X  1  1 X^2+X+1 X^3+1  1 X^3+X^2 X^2+X  1 X^3+X^2+X X^2 X^3+X^2+1 X^3 X^3+X^2  1 X^2+X X^2+X+1  1  0 X^2+X X^3+X^2+1  X  0 X^3 X^2+X+1  1  1  1  1 X^2+X  1 X^2+X X^3  1 X^2  0  X X^2+1 X^3+1  1 X^3+1  0
 0  0  1  0  0 X^3 X^3+X+1 X+1 X^3+1 X^2+1 X+1 X^2  1  1  0 X^3 X^3+X^2+X X^2+1 X^2+X+1 X^3+X^2  1 X^2+X+1 X^3+X  1 X^3+X^2+1  1 X^3+X+1 X^2 X^3+X^2+X X^3+X  1 X^2+X+1 X^2+X X^3+X^2+1 X^3+X^2 X^2+X+1  1 X^3+1 X^3+X X^2  0 X^3+X^2+X X^2 X+1  1 X^2+X X^3+X^2+X+1 X+1 X^2+1  1 X^3+X^2+X+1 X^3+X+1  X  1 X^3+X+1  0 X^2+X  0 X^3+X^2+1 X^3+X^2+1  X X^3+1 X^3+X^2+X  0  1 X^3 X^3+1 X^3+X  X X^3 X^3+1 X^3
 0  0  0  1  1 X^3+X+1 X+1 X^3+1  X X^3 X^3+X^2+X+1 X^3+1 X^3+X+1 X^3+X^2+X X^3+X  1  0 X^3+X^2 X+1 X^2+X+1  1 X^3+X X^3+X X^3+X^2+X+1 X^2+1 X^3 X^3+X^2+1 X^2 X^2+1 X^3+1 X^3+X+1 X^3+X^2+X+1  1 X+1 X^3+1 X^3 X^2+X X^2 X^2+X X^3+X^2+X+1 X^3+X X^2+X  1 X^3+X^2+X X^3+X^2+1  0  0 X^2+X X^3+1 X^3 X^3+X^2 X^2+1  1 X^2+1 X^2+X+1 X^3+X^2+X X^2 X^3+X^2  0 X^3+1 X^2  X X^3+1 X^3+X^2+1  0  1 X^3+X+1  1 X^3+1  1  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+187x^64+1314x^65+2624x^66+4962x^67+7453x^68+10686x^69+12974x^70+16814x^71+16652x^72+17260x^73+13622x^74+10980x^75+6976x^76+4402x^77+2188x^78+1154x^79+406x^80+210x^81+126x^82+38x^83+19x^84+12x^85+2x^86+4x^87+2x^88+4x^89

The gray image is a linear code over GF(2) with n=576, k=17 and d=256.
This code was found by Heurico 1.16 in 165 seconds.