The generator matrix

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

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+119x^60+104x^61+369x^62+208x^63+450x^64+316x^65+425x^66+308x^67+418x^68+272x^69+343x^70+232x^71+227x^72+76x^73+111x^74+20x^75+34x^76+22x^78+21x^80+8x^82+8x^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 1.03 seconds.