The generator matrix

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

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+164x^67+241x^68+280x^69+116x^70+324x^71+166x^72+182x^73+63x^74+136x^75+86x^76+78x^77+31x^78+60x^79+36x^80+26x^81+13x^82+20x^83+12x^84+10x^85+1x^86+1x^88+1x^92

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 0.358 seconds.