The generator matrix

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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+57x^82+90x^83+185x^84+324x^85+348x^86+460x^87+579x^88+554x^89+636x^90+664x^91+592x^92+670x^93+601x^94+558x^95+531x^96+378x^97+330x^98+222x^99+129x^100+94x^101+41x^102+42x^103+13x^104+20x^105+20x^106+6x^107+12x^108+8x^109+9x^110+4x^111+4x^112+3x^114+2x^115+2x^116+1x^118+2x^122

The gray image is a linear code over GF(2) with n=368, k=13 and d=164.
This code was found by Heurico 1.16 in 7.03 seconds.