The generator matrix

 1  0  0  1  1  1  0  X  1 X^2  1  1  1  0  1  1  1  X X^2+X  1  0  1  1  X  1 X^2+X  X X^2+X  1 X^2  1  1  X  1  1  1 X^2 X^2+X  1 X^2+X X^2  X  1  1  1  1  0 X^2  1  1  1 X^2+X  1  1  1 X^2+X X^2+X  1  1 X^2+X  X X^2+X  1  1 X^2  1  0 X^2  1  1  1 X^2
 0  1  0  0  1  1  1 X^2 X^2+1  1 X^2 X^2+X+1 X^2  1 X+1 X^2 X^2+X+1  1  0  0  1 X^2+1  1  1  0  1 X^2+X  1 X^2  X X^2+X  1  1  X X^2+1 X^2+X X^2+X  1 X+1 X^2+X  1  1 X^2+X X^2+1 X^2+X X+1  1  1 X^2+X X+1  X X^2+X X^2+1 X+1  0  1  1 X+1 X+1  0  1  1 X^2+X+1  0 X^2  X  1  0 X^2+1 X^2+X X^2  X
 0  0  1  1 X^2 X^2+1  1  1  0 X^2 X^2 X^2+1  1 X^2+1 X^2+X X^2+X  1 X^2+X+1  1 X+1  X X^2+X+1 X^2+X  0 X^2+X+1  1  1  1  X  1 X+1  X  1  0 X^2+1  X  1 X+1  X  1 X^2+X+1 X^2+X X+1 X^2+X+1 X^2+X X^2+X+1 X+1 X^2+X  1  0 X^2+1  1  X  X X+1 X^2+X  X X^2+1 X^2+X+1  1 X^2+1  0 X^2 X^2+1  1  X X^2  1  0 X^2+X+1  X  0
 0  0  0  X  0  X  X  X  X  X  X X^2 X^2 X^2 X^2  0 X^2+X  X  0 X^2 X^2+X  0 X^2+X X^2 X^2+X X^2+X X^2+X X^2 X^2+X  0  X  0  0  0 X^2 X^2 X^2+X  0  X X^2 X^2+X  X X^2 X^2+X X^2+X X^2  0 X^2  0 X^2+X X^2+X  X  X  0  X X^2 X^2+X  X  X  X  X  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2  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+142x^67+234x^68+270x^69+275x^70+202x^71+182x^72+128x^73+118x^74+104x^75+90x^76+70x^77+54x^78+48x^79+37x^80+44x^81+30x^82+12x^83+3x^86+2x^87+2x^91

The gray image is a linear code over GF(2) with n=288, k=11 and d=134.
This code was found by Heurico 1.11 in 0.203 seconds.