The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+46x^58+78x^59+115x^60+170x^61+202x^62+226x^63+329x^64+358x^65+383x^66+460x^67+364x^68+346x^69+265x^70+170x^71+150x^72+112x^73+82x^74+66x^75+59x^76+32x^77+37x^78+24x^79+4x^80+6x^81+8x^82+2x^84+1x^106

The gray image is a linear code over GF(2) with n=268, k=12 and d=116.
This code was found by Heurico 1.16 in 1.36 seconds.