The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+158x^71+618x^72+1228x^73+1999x^74+2886x^75+3841x^76+5030x^77+6325x^78+7900x^79+8702x^80+9780x^81+11014x^82+11320x^83+11170x^84+10430x^85+9384x^86+7944x^87+6410x^88+4684x^89+3721x^90+2642x^91+1699x^92+1062x^93+411x^94+324x^95+187x^96+98x^97+42x^98+40x^99+10x^100+4x^101+2x^103+2x^104+2x^105+2x^109

The gray image is a linear code over GF(2) with n=332, k=17 and d=142.
This code was found by Heurico 1.13 in 274 seconds.