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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+57x^54+50x^55+144x^56+148x^57+256x^58+284x^59+437x^60+562x^61+687x^62+946x^63+1098x^64+1326x^65+1451x^66+1532x^67+1429x^68+1364x^69+1122x^70+950x^71+690x^72+560x^73+360x^74+292x^75+222x^76+122x^77+111x^78+38x^79+47x^80+14x^81+43x^82+4x^83+21x^84+7x^86+4x^88+2x^90+3x^92

The gray image is a linear code over GF(2) with n=268, k=14 and d=108.
This code was found by Heurico 1.16 in 21.7 seconds.