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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+53x^68+56x^69+177x^70+240x^71+314x^72+396x^73+443x^74+592x^75+772x^76+950x^77+1037x^78+1240x^79+1268x^80+1374x^81+1388x^82+1230x^83+1063x^84+884x^85+715x^86+540x^87+452x^88+328x^89+255x^90+184x^91+124x^92+94x^93+61x^94+60x^95+45x^96+14x^97+17x^98+10x^99+4x^100+2x^102+1x^114

The gray image is a linear code over GF(2) with n=324, k=14 and d=136.
This code was found by Heurico 1.16 in 27.3 seconds.