The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X  1  1  X  X  X  X  1  1 X^2  1  1  0  0  1  1  1  1 X^2  1  0  1  1  1  X  0  1 X^2  X  1  1  0 X^2+X  X  1  1  1  1  0  X  1 X^2+X  1  1  1  1 X^2+X  0 X^2+X  1 X^2+X X^2+X  1  1 X^2  1 X^2  1
 0  1  0  X  1 X^2+X+1  1 X^2+X  0 X^2  1 X+1  1  1 X^2+X  1 X^2+X+1  X  1  0 X^2+1  1  1 X^2+X X^2+1 X+1 X^2  0 X+1 X^2+X  0 X^2+1 X^2+X  1  0  X  1  1 X^2+1 X^2+X+1 X^2+X  X  1 X^2  1 X^2+X+1 X^2+X+1 X^2 X^2  0  1 X^2+X+1  X X^2+X+1 X+1  1  1  1  0  1 X^2 X^2+X+1  1  1 X^2 X^2+X  0
 0  0  1  1 X^2+X+1 X^2+X  1 X+1 X^2+X  1 X^2+1  0  0 X+1  1  X  1  X X^2+1 X+1  0 X^2+X X+1 X+1  X X+1 X^2+1  1  X  1 X^2 X^2+X+1 X^2+1 X^2+X+1  1 X^2 X^2  1  X X^2+X+1  1  1  1 X+1 X^2+X  1 X^2+1  1  1  1  0  1 X^2  1  0 X+1  0  X X^2+X X^2+X  1 X^2+X+1  X  X X^2+X+1  1  0
 0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 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+41x^60+178x^61+209x^62+450x^63+372x^64+428x^65+383x^66+362x^67+284x^68+362x^69+203x^70+244x^71+157x^72+152x^73+77x^74+90x^75+34x^76+32x^77+20x^78+6x^79+6x^80+4x^82+1x^84

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 0.831 seconds.