The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+20x^65+91x^66+8x^67+27x^68+16x^69+65x^70+8x^71+3x^72+8x^73+1x^74+1x^76+3x^78+4x^81

The gray image is a linear code over GF(2) with n=272, k=8 and d=130.
This code was found by Heurico 1.16 in 31.6 seconds.