The generator matrix

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

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+357x^68+335x^72+308x^76+15x^80+6x^84+1x^88+1x^132

The gray image is a linear code over GF(2) with n=288, k=10 and d=136.
This code was found by Heurico 1.16 in 6.69 seconds.