The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+242x^61+386x^62+544x^63+603x^64+826x^65+726x^66+648x^67+664x^68+656x^69+557x^70+628x^71+424x^72+462x^73+284x^74+242x^75+143x^76+82x^77+27x^78+16x^79+18x^80+4x^81+4x^82+2x^83+3x^84

The gray image is a linear code over GF(2) with n=272, k=13 and d=122.
This code was found by Heurico 1.11 in 1.16 seconds.