The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+104x^61+334x^62+458x^63+408x^64+410x^65+394x^66+350x^67+346x^68+252x^69+213x^70+220x^71+153x^72+130x^73+126x^74+78x^75+48x^76+32x^77+19x^78+14x^79+4x^80+2x^82

The gray image is a linear code over GF(2) with n=268, k=12 and d=122.
This code was found by Heurico 1.16 in 0.714 seconds.