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  1  0 X^2  1  1  X  X  1  0  X  X X^2  1  X  1  X X^2  1  X X^2  0  0  0  1  1  X  X X^2
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  0 X^2+X  X X^2 X^2+X X^2+X  0  0  X X^2+X X^2+X  0  0 X^2+X  X X^2  0  0  X  X  X  X  X  X  0 X^2+X X^2 X^2  X  X  0 X^2 X^2  0  X  X X^2  X X^2 X^2+X X^2+X  X  X X^2+X X^2+X  X  0 X^2  X  0 X^2  X X^2  0
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X X^2+X X^2 X^2+X X^2 X^2 X^2  0  X  X X^2 X^2+X X^2  X  X X^2  X X^2+X  0  X X^2+X X^2+X X^2+X X^2+X X^2+X  X X^2+X X^2+X  X  X X^2+X X^2+X X^2+X  0 X^2  0  X  0  X  X  X X^2  0  0 X^2  0 X^2  X  X  0 X^2 X^2+X  0  X  X
 0  0  0  X  X  0 X^2+X  X  0  X  0  X X^2+X X^2+X X^2 X^2  0 X^2  X X^2+X  0  0 X^2+X X^2+X  X  0  X  0  X  X  0  0 X^2 X^2  0  0  X X^2 X^2 X^2+X  0 X^2 X^2  X X^2+X  X X^2 X^2  0  X X^2  X X^2+X  X  X  X X^2+X  0  X X^2  0 X^2 X^2+X  0 X^2+X  0  X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 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+244x^56+426x^58+36x^59+850x^60+192x^61+1066x^62+456x^63+1618x^64+824x^65+1940x^66+1040x^67+2070x^68+856x^69+1570x^70+504x^71+1094x^72+168x^73+662x^74+12x^75+410x^76+8x^77+210x^78+96x^80+12x^82+14x^84+2x^86+2x^88+1x^96

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 27.3 seconds.