The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+80x^83+542x^84+962x^85+1658x^86+2306x^87+3385x^88+3904x^89+5323x^90+6092x^91+7630x^92+8246x^93+9483x^94+10158x^95+10764x^96+10274x^97+10490x^98+8234x^99+7970x^100+6206x^101+5220x^102+3906x^103+2959x^104+1918x^105+1379x^106+804x^107+554x^108+252x^109+151x^110+94x^111+43x^112+40x^113+24x^114+6x^115+8x^116+6x^117

The gray image is a linear code over GF(2) with n=384, k=17 and d=166.
This code was found by Heurico 1.13 in 317 seconds.