The generator matrix

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

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+51x^56+102x^57+141x^58+332x^59+319x^60+684x^61+561x^62+1254x^63+904x^64+1766x^65+1145x^66+1936x^67+1132x^68+1824x^69+902x^70+1300x^71+493x^72+618x^73+228x^74+276x^75+140x^76+116x^77+69x^78+22x^79+23x^80+10x^81+21x^82+8x^84+4x^86+1x^90+1x^92

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 15.9 seconds.