The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+174x^71+554x^72+1128x^73+1335x^74+2136x^75+2535x^76+3374x^77+3490x^78+4996x^79+4896x^80+5376x^81+5221x^82+5920x^83+4719x^84+5104x^85+3793x^86+3392x^87+2376x^88+2010x^89+1108x^90+820x^91+465x^92+264x^93+173x^94+86x^95+33x^96+22x^97+16x^98+10x^99+5x^100+2x^101+2x^107

The gray image is a linear code over GF(2) with n=328, k=16 and d=142.
This code was found by Heurico 1.13 in 67.9 seconds.