The generator matrix

 1  0  0  0  1  1  1 X^2  X  1  1  0 X^2  1  1  1 X^2+X X^2+X X^2  1  1  1  1 X^2 X^2+X  1 X^2+X  1  1  0  1  1  1 X^2+X  0 X^2  1  1  1  1 X^2  X  1  0  1 X^2+X  1  1 X^2+X  1 X^2  0  1 X^2+X  X  1  1 X^2+X  0 X^2+X  0  0  1  1  0  1  1
 0  1  0  0  1 X^2  1  0  1  1 X^2  1  1  X  1 X^2+X  1  1  X X+1 X^2+X X^2+X X^2+X+1 X^2+X  X X^2+1  1  1  X  1  0  1 X+1  0  X  1 X^2 X+1 X+1  1  0  1  X  1 X^2+X  1 X^2  0  1  X  0  1 X^2+X+1  X  1 X^2  X  1  1  1  1 X^2 X^2+X+1  X  1  0 X^2+1
 0  0  1  0  X  0 X^2+X  1 X^2 X^2+X+1  1 X^2+X+1 X^2+X+1  1 X^2+1 X+1  1 X^2  1  0 X^2+X  0  X X^2  1 X^2+1 X^2+X+1  1 X+1  0 X^2+1  0 X^2+X  1  1  1 X^2+1  1 X^2+X X+1  X X^2+X X^2+X+1 X^2+X+1 X^2+X+1 X^2+X X^2+X  X X^2+X+1 X^2  1 X^2+1 X^2+X+1  1 X^2+1 X+1 X^2 X^2+1  0  X X+1  1 X^2+X+1 X^2+1 X^2  0 X^2+X+1
 0  0  0  1  X  1 X+1  1  1 X^2+1 X^2+X X^2+X X+1 X+1 X^2  0 X^2+1 X^2+X+1  0 X^2+X X^2+X X+1 X^2+X+1  1 X^2+X+1 X^2+X+1 X^2  X  1  X X+1 X+1  0  0  1  0 X^2+1 X^2 X^2+X X^2  1 X^2+1 X+1  X  X X^2+X X^2+1 X^2+X X^2+X X^2+1  X  0 X^2+1  X  0 X^2+X+1 X^2+X X^2+X+1  1  1 X^2+X+1 X^2 X^2+1 X+1 X^2+X X+1 X^2+1
 0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  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  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 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+190x^60+400x^61+591x^62+670x^63+699x^64+734x^65+685x^66+682x^67+601x^68+656x^69+569x^70+482x^71+410x^72+310x^73+240x^74+94x^75+73x^76+60x^77+26x^78+8x^79+8x^80+1x^82+2x^84

The gray image is a linear code over GF(2) with n=268, k=13 and d=120.
This code was found by Heurico 1.11 in 1.13 seconds.