The generator matrix

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

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+127x^60+72x^61+414x^62+124x^63+569x^64+204x^65+554x^66+224x^67+433x^68+192x^69+436x^70+156x^71+347x^72+44x^73+94x^74+8x^75+28x^76+28x^78+26x^80+8x^82+3x^84+2x^86+1x^88+1x^92

The gray image is a linear code over GF(2) with n=268, k=12 and d=120.
This code was found by Heurico 1.16 in 0.977 seconds.