The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  X  0  1  0  1  1  1  X  0  0  1  1  1  X  1  1  0  1  1  1  0  0  1  1  X  X  0  1  1  1  X  1  1  0  1  1  1  0  1  1  X  0  1  0  X  1  0  1  0  X  0  1  0  X  0  0  1  1  1  X  X  1  0  0  X  1  1  1  0  0  1  X  1  1  1  1  1  0  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  X  0  0  0  1  X  1 X+1  1  1  0  0  1  0  X X+1  X  X  0  1  X  0 X+1  0  1  X  0  1  1  1  0  1  X  1 X+1 X+1  X X+1  0 X+1  1  1 X+1  0  X  1  1  1 X+1  0  X  1  1  1  1  1  1  1  X  0  X  0  1  1  X  1  1  0 X+1  1  0  X  0  X  0  X  0  1  0  1  1  0
 0  0  1  0  1  1  0  1  0  1  1  X  0  1  1  X  1  X  X  1  1 X+1  0  1  1  1  0  0  1  X  1  0  1  X  0  1 X+1  1 X+1  1  1 X+1 X+1  X X+1  0  0  X  X  X  1  1 X+1  1  X  1 X+1  X  0  1 X+1 X+1  X  1  0  X  0  0  X  X X+1  1  X  X X+1  0 X+1  1  X  0  0  0 X+1  X  X  X  1  1  1  0  1  1  1  X  1  0
 0  0  0  1  1  0  1  1  1  0 X+1  X  1  X  1 X+1  0  1  0 X+1  0  0  1 X+1  0  X  1  X  0  X  1  1  0  1  0  X  0  1  1 X+1  1  X X+1  1  0  X  1  X  0 X+1  0  X  1  1  1  1  0  1  1 X+1 X+1  X  0  X X+1  X  X  X  0  0 X+1 X+1  1  1 X+1  X X+1  1 X+1  X X+1  1  X  0  X  1  X  1  X  0  0 X+1  1  1  1  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  X  X  X  X  0  X  0  0  X  0  0  X  X  0  0  0  0  X  0  0  0  X  0  X  X  X  X  0  X  0  X  X  X  0  X  0  0  0  X  X  0  0  X  X  0  X  X  0  X  0  0  0  X  0  0  X  0  X  X  0  X  X  X  0  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  0  0  X  0  0  X  X  0  X  0  X  0  0  X  0  X  0  X  0  0  X  X  0  0  X  X  0  0  X  0  0  0  X  0  0  X  X  0  X  0  0  X  0  0  X  X  0  0  X  X  X  X  X  0  0  X  0  0  X  X  X  X  X  0  X  X  0  0  X  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  X  0  0  X  0  X  X  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  X  0  X  X  0  X  X  X  0  0  X  X  0  0  X  X  0  0  X  0  0  X  X  0  0  X  0  0  0  0  0  X  X  X  X  0  0  X  X  0  X  X  0  0  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  X  X  X  X  0  0  X  X  0  X  X  0  X  X  0  X  0  X  0  X  X  X  0  X  X  0  0  X  0  0  X  X  0  0  X  0  0  0  0  0  X  0  0  0  0  X  0  X  0  X  0  X  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0  X  X  0  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  0  0  X  0  0  X  0  X  X  X  X  X  X  0  X  0  X  0  X  X  0  X  0  0  0  0  X  0  X  X  X  X  0  0  X  X  X  0  0  X  0  X  0  X  X  0  X  0  0  0  0  0  0  X  0  X  0  0  X  X  X  X  X  0  X  X  X  0  X  X  X  0  0  X  0

generates a code of length 96 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+35x^82+70x^83+150x^84+172x^85+252x^86+270x^87+334x^88+378x^89+338x^90+382x^91+378x^92+394x^93+450x^94+434x^95+406x^96+388x^97+355x^98+392x^99+358x^100+408x^101+321x^102+298x^103+240x^104+202x^105+189x^106+158x^107+127x^108+82x^109+77x^110+38x^111+39x^112+24x^113+26x^114+6x^115+10x^116+3x^118+4x^120+1x^122+1x^124+1x^126

The gray image is a linear code over GF(2) with n=192, k=13 and d=82.
This code was found by Heurico 1.16 in 17.1 seconds.