The generator matrix

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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+72x^60+210x^61+398x^62+568x^63+608x^64+670x^65+676x^66+704x^67+694x^68+678x^69+676x^70+560x^71+507x^72+338x^73+256x^74+244x^75+149x^76+78x^77+32x^78+32x^79+10x^80+6x^81+8x^82+4x^83+5x^84+2x^85+2x^86+2x^88+2x^89

The gray image is a linear code over GF(2) with n=272, k=13 and d=120.
This code was found by Heurico 1.16 in 3.24 seconds.