The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+129x^64+140x^65+164x^66+108x^67+148x^68+44x^69+84x^70+32x^71+36x^72+28x^73+44x^74+20x^75+14x^76+12x^77+12x^78+6x^80+2x^84

The gray image is a linear code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 0.181 seconds.