The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+72x^56+38x^58+24x^59+357x^60+184x^61+312x^62+472x^63+954x^64+992x^65+938x^66+1552x^67+1437x^68+1744x^69+1424x^70+1552x^71+1121x^72+992x^73+714x^74+472x^75+440x^76+184x^77+152x^78+24x^79+146x^80+6x^82+49x^84+25x^88+5x^92+1x^96

The gray image is a linear code over GF(2) with n=276, k=14 and d=112.
This code was found by Heurico 1.16 in 16.2 seconds.