The generator matrix

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

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+349x^64+440x^65+890x^66+892x^67+1244x^68+1112x^69+1512x^70+1180x^71+1485x^72+1280x^73+1340x^74+992x^75+1212x^76+736x^77+688x^78+396x^79+300x^80+104x^81+138x^82+28x^83+36x^84+8x^85+8x^86+9x^88+4x^92

The gray image is a linear code over GF(2) with n=288, k=14 and d=128.
This code was found by Heurico 1.13 in 104 seconds.