The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+46x^59+157x^60+174x^61+364x^62+302x^63+695x^64+480x^65+883x^66+574x^67+997x^68+544x^69+915x^70+450x^71+599x^72+274x^73+337x^74+136x^75+79x^76+56x^77+38x^78+24x^79+22x^80+6x^81+17x^82+4x^83+7x^84+2x^85+3x^86+3x^88+3x^90

The gray image is a linear code over GF(2) with n=272, k=13 and d=118.
This code was found by Heurico 1.16 in 68.6 seconds.