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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+207x^56+458x^58+48x^59+744x^60+308x^61+816x^62+844x^63+950x^64+1840x^65+960x^66+2056x^67+1052x^68+1928x^69+872x^70+848x^71+802x^72+272x^73+530x^74+40x^75+486x^76+4x^77+184x^78+4x^79+103x^80+20x^82+5x^84+1x^88+1x^100

The gray image is a linear code over GF(2) with n=268, k=14 and d=112.
This code was found by Heurico 1.16 in 22 seconds.