The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+146x^67+168x^68+366x^69+221x^70+262x^71+147x^72+166x^73+72x^74+98x^75+56x^76+116x^77+45x^78+76x^79+30x^80+32x^81+14x^82+8x^83+14x^84+6x^85+2x^87+2x^89

The gray image is a linear code over GF(2) with n=288, k=11 and d=134.
This code was found by Heurico 1.16 in 0.359 seconds.