The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  0  1  1 X^2  X  1  1  1  X  1  1  1  0  1  1 X^2  0  0  X  X X^2+X  X  1  1  X  1  1  0  1  1  1  0 X^2 X^2+X X^2  1  1  1  1 X^2+X  1  X  0  0  X  1 X^2+X  1 X^2 X^2+X X^2+X  X  1 X^2+X  1  1  1 X^2+X X^2+X X^2+X X^2  0
 0  1  0  0  X  X X^2+X  0  1 X^2+1  1 X^2+X+1 X+1  1  1 X^2+X X^2 X^2+1  X  X X^2+X+1 X^2+X+1 X^2  0 X^2+1  1  X  1  1  1 X^2+X  X  X  X  1  1 X^2+X+1 X^2 X^2+1 X+1 X^2+X  1 X^2+X  1  X  0 X^2+X  X X^2+X  1  1 X^2  1 X^2+X  0 X^2  1 X+1  1  X  1  1 X^2  1 X+1  0 X^2  0  0 X^2  0  1
 0  0  1  0  X X^2+X+1 X^2+X+1  1 X+1  0  X  X  1 X^2+X+1 X^2+1 X^2 X^2+1 X+1  X X+1 X^2+X+1  0  1 X^2+X X^2  0  1 X^2+1  1  X  0  1  0 X^2+X X^2 X^2+X  1  1 X+1  X X^2+X+1 X+1  1 X+1 X^2 X^2+1 X^2+X X^2 X^2+1 X^2  0  1  X X^2  1 X+1  0 X+1 X^2+X+1  1 X^2+X  0 X+1 X^2+1  0  X  0  1  1  1  X  0
 0  0  0  1 X+1 X^2+X+1  X  1  X X+1 X+1 X^2+X  1 X^2+1  X  0 X^2+X X^2  1 X^2+1  1 X^2+X+1 X+1 X^2+X+1 X^2+X X+1  X  0 X^2+1 X^2+X  1  1 X^2+X+1  X X+1 X^2 X+1  X X^2+X  1 X^2 X^2 X^2+X X+1  1 X+1  1 X^2+X X^2 X^2 X^2 X+1  1  1 X^2+X+1  0  0  X X^2+1  1 X^2+X+1 X^2+1 X+1 X+1 X^2+X X+1  X  1 X^2 X+1  1  1
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 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+240x^65+439x^66+536x^67+693x^68+698x^69+707x^70+704x^71+710x^72+616x^73+533x^74+566x^75+467x^76+352x^77+325x^78+248x^79+131x^80+88x^81+69x^82+38x^83+14x^84+6x^85+6x^86+4x^87+1x^90

The gray image is a linear code over GF(2) with n=288, k=13 and d=130.
This code was found by Heurico 1.16 in 14.6 seconds.