The generator matrix

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

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+232x^61+410x^62+574x^63+568x^64+766x^65+707x^66+730x^67+633x^68+670x^69+606x^70+586x^71+488x^72+430x^73+265x^74+218x^75+93x^76+106x^77+58x^78+32x^79+9x^80+4x^81+2x^82+4x^83

The gray image is a linear code over GF(2) with n=272, k=13 and d=122.
This code was found by Heurico 1.16 in 3.09 seconds.