The generator matrix

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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+76x^78+408x^79+898x^80+1340x^81+2278x^82+3028x^83+3921x^84+5124x^85+6333x^86+7658x^87+8751x^88+9766x^89+10207x^90+10734x^91+10606x^92+9964x^93+9132x^94+7978x^95+6767x^96+4998x^97+3632x^98+2826x^99+1801x^100+1072x^101+769x^102+420x^103+247x^104+170x^105+75x^106+36x^107+24x^108+8x^109+10x^110+8x^112+6x^113

The gray image is a linear code over GF(2) with n=364, k=17 and d=156.
This code was found by Heurico 1.13 in 302 seconds.