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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+130x^84+560x^85+868x^86+1748x^87+2363x^88+3424x^89+3877x^90+5126x^91+6391x^92+7720x^93+8273x^94+9714x^95+9807x^96+10358x^97+9925x^98+10386x^99+8543x^100+8078x^101+6219x^102+5374x^103+3970x^104+2982x^105+1864x^106+1306x^107+818x^108+558x^109+316x^110+182x^111+77x^112+44x^113+18x^114+14x^115+26x^116+4x^117+6x^119+2x^120

The gray image is a linear code over GF(2) with n=388, k=17 and d=168.
This code was found by Heurico 1.13 in 323 seconds.