The generator matrix

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

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+100x^65+207x^66+276x^67+314x^68+324x^69+399x^70+366x^71+298x^72+352x^73+351x^74+292x^75+254x^76+218x^77+164x^78+68x^79+16x^80+20x^81+25x^82+10x^83+8x^84+6x^85+4x^86+10x^87+4x^88+4x^89+1x^90+2x^91+1x^96+1x^102

The gray image is a linear code over GF(2) with n=288, k=12 and d=130.
This code was found by Heurico 1.16 in 3.38 seconds.