The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+236x^73+677x^74+1318x^75+1752x^76+3124x^77+3678x^78+5562x^79+6181x^80+8070x^81+8392x^82+10416x^83+9839x^84+11672x^85+10278x^86+11232x^87+8626x^88+8190x^89+6112x^90+5482x^91+3534x^92+2694x^93+1598x^94+1122x^95+552x^96+358x^97+164x^98+120x^99+35x^100+20x^101+6x^102+12x^103+8x^104+2x^105+7x^106+2x^109

The gray image is a linear code over GF(2) with n=340, k=17 and d=146.
This code was found by Heurico 1.13 in 282 seconds.