The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+296x^65+300x^66+690x^67+477x^68+856x^69+593x^70+904x^71+560x^72+742x^73+452x^74+722x^75+302x^76+442x^77+215x^78+256x^79+117x^80+146x^81+33x^82+50x^83+13x^84+14x^85+4x^86+2x^88+3x^90+2x^91

The gray image is a linear code over GF(2) with n=288, k=13 and d=130.
This code was found by Heurico 1.11 in 28.9 seconds.