The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  0  1  1 X^2+X  1  1  0  1  1  1  1 X^2+X  1  0  1  1  1 X^2+X  1 X^2+X  1  1  0  1 X^2+X  1  1  1  1  1  1  0  1  X X^2+X  1  1  1 X^2+X  1  1  1  1  X  1  1  1  1  X  X X^2+X  1  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  1  0 X^2+1  1 X^2+X X+1  1 X+1  0 X^2+1 X^2+X  1 X+1  1 X^2 X^2+X X^2+1  1  0  1 X^2+1  X  1 X+1  1  0 X^2+1 X+1 X^2+X+1 X^2+X X^2+1  1  0  1  1  0 X^2+X X^2+1  1  1 X+1 X+1 X^2+X+1  1 X^2+X+1 X^2+X  1 X+1  1  1  1 X+1  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 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 X^2  0  0  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 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+46x^56+16x^57+66x^58+68x^59+329x^60+240x^61+388x^62+432x^63+786x^64+512x^65+964x^66+536x^67+1029x^68+512x^69+680x^70+432x^71+454x^72+240x^73+202x^74+68x^75+109x^76+16x^77+4x^78+36x^80+19x^84+4x^88+2x^92+1x^96

The gray image is a linear code over GF(2) with n=268, k=13 and d=112.
This code was found by Heurico 1.16 in 4.29 seconds.