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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+76x^54+156x^56+4x^57+240x^58+12x^59+520x^60+124x^61+838x^62+340x^63+1296x^64+616x^65+1948x^66+952x^67+2209x^68+952x^69+1951x^70+616x^71+1342x^72+340x^73+727x^74+124x^75+442x^76+12x^77+268x^78+4x^79+127x^80+74x^82+45x^84+19x^86+4x^88+3x^90+2x^96

The gray image is a linear code over GF(2) with n=272, k=14 and d=108.
This code was found by Heurico 1.16 in 29.1 seconds.