The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  0  X  1  1  X  1  1  X  X  1  1 X^2 X^2+X  1  0  1  1  1  1  1  1  0  1  1  1  X  1  1  1  1  X  X  0  1  X  1  X  1 X^2 X^2  0 X^2  X X^2  X  X  0  0  1  1  1  X  1  1  1  X  1  1  1
 0  1  0  0  1 X+1  1 X^2+X X^2+1  1  X X^2+1 X^2+X  1 X^2+X+1  0 X^2  1 X+1  X  1  1 X^2  X X^2+X X^2+X+1  0 X^2+X+1 X+1 X+1 X^2  1  X X+1  1 X^2 X^2+1  0  X X^2  1  1 X+1  1 X^2+X  1 X^2+X+1  1  1 X^2+X  1  0  1  X X^2+X  1  0 X^2 X^2  1  1  X X^2+1 X^2+1  1  X  0 X^2
 0  0  1  1  1  0  1  1 X^2+1 X^2+1  1  0 X^2  X  1  X  1 X^2+X X^2+X  1  1 X^2  0  1  1 X^2+1  X  0 X^2+X+1 X^2+X  1 X^2+X+1 X^2+X+1  X X^2 X+1  0 X^2 X^2+X+1  1 X^2+X  X X+1 X^2+1  0 X+1 X+1 X^2+X+1  X  1  X  1 X^2  1  1  1  1 X^2+X X+1  X X^2 X^2+X  X X^2 X^2 X^2+X X^2+X X^2
 0  0  0  X  0  0 X^2 X^2 X^2+X  X  X  X  X X^2+X X^2+X X^2  0  0  0 X^2  X X^2+X X^2+X X^2+X X^2+X X^2 X^2  X X^2 X^2+X  0 X^2  0  X X^2 X^2+X X^2+X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2  0 X^2+X X^2+X  0 X^2 X^2 X^2 X^2+X  X X^2 X^2 X^2+X  X X^2  0  X X^2 X^2 X^2 X^2+X X^2 X^2+X X^2
 0  0  0  0  X X^2  X X^2+X X^2 X^2 X^2+X X^2+X  X X^2+X X^2+X  X  X X^2+X X^2+X  0  X  0  0 X^2  X  0 X^2  0  X  X  X  0  0  0  X X^2  X  X X^2+X  X  0 X^2+X  0 X^2  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2  X X^2  X  X  X X^2+X X^2+X X^2  X X^2+X  X  0  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+38x^60+270x^61+331x^62+522x^63+589x^64+802x^65+607x^66+768x^67+573x^68+784x^69+617x^70+726x^71+433x^72+396x^73+226x^74+238x^75+103x^76+62x^77+31x^78+16x^79+17x^80+18x^81+11x^82+2x^83+6x^84+4x^85+1x^86

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 3.36 seconds.