The generator matrix

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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+120x^83+282x^84+536x^85+582x^86+658x^87+618x^88+756x^89+587x^90+600x^91+486x^92+538x^93+515x^94+448x^95+349x^96+312x^97+206x^98+236x^99+129x^100+86x^101+53x^102+38x^103+18x^104+10x^105+9x^106+12x^107+5x^108+2x^113

The gray image is a linear code over GF(2) with n=364, k=13 and d=166.
This code was found by Heurico 1.11 in 1.77 seconds.