The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+126x^68+126x^69+212x^70+84x^71+126x^72+92x^73+32x^74+44x^75+62x^76+18x^77+24x^78+16x^79+29x^80+4x^81+16x^82+8x^84+4x^86

The gray image is a linear code over GF(2) with n=288, k=10 and d=136.
This code was found by Heurico 1.11 in 0.156 seconds.