The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+439x^60+924x^62+1445x^64+1446x^66+1476x^68+1102x^70+736x^72+390x^74+161x^76+38x^78+26x^80+4x^82+2x^84+2x^92

The gray image is a linear code over GF(2) with n=268, k=13 and d=120.
This code was found by Heurico 1.16 in 17.8 seconds.