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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+64x^72+92x^73+200x^74+260x^75+309x^76+404x^77+498x^78+636x^79+708x^80+888x^81+1044x^82+1168x^83+1250x^84+1274x^85+1310x^86+1270x^87+1145x^88+968x^89+674x^90+526x^91+427x^92+314x^93+259x^94+194x^95+147x^96+122x^97+90x^98+38x^99+38x^100+32x^101+19x^102+4x^103+7x^104+2x^105+1x^110+1x^118

The gray image is a linear code over GF(2) with n=340, k=14 and d=144.
This code was found by Heurico 1.16 in 29.3 seconds.