The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 X 1 1 X 0 0 X 1 X 1 0 1 1 X X 1 1 1 1 X 1 X 0 1 X X 1 1 1 0 1 1 X 1 0 X 0 1 1 1 1 1 X 0 0 1 1 X 0 1 1 1 X 0 1 1 X 1 1 X 1 1 1 1 1 1 0 1 1 X 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 1 0 X+1 1 X 1 0 X+1 X 1 X 0 0 1 1 1 1 1 0 1 X+1 X 1 X+1 1 1 1 X+1 0 X X+1 X 1 X+1 1 1 X 0 1 1 X 1 X X 1 0 0 X 1 1 1 1 X 1 X X+1 X 0 0 1 X 0 X 0 X 1 1 1 0 X 1
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 0 1 1 X+1 1 X+1 1 X+1 X 1 X X 0 0 X X 0 0 0 0 1 0 X+1 1 1 1 X+1 1 X X X X+1 0 X+1 X 1 X+1 X+1 X+1 0 1 1 1 X 1 X X+1 1 X+1 1 1 X X+1 X 1 X 1 X X+1 1 0 0 0 X+1 X+1 X+1 X 1 X+1
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 0 1 0 1 X+1 X 0 X+1 1 1 1 0 X 1 X X+1 1 X+1 0 X X 1 X 0 1 X+1 1 X X+1 X 1 0 0 X X+1 X X 0 X+1 X X X X+1 X+1 X X X 1 1 0 1 X+1 X 1 X 0 0 1 X 1 1 X+1 X 1 X X+1 1 X+1 X+1 0 X+1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 1 X+1 1 X+1 X 0 1 0 X X 1 0 X+1 0 X+1 1 X 1 0 0 X 1 1 X 0 X 1 1 1 1 1 0 X+1 1 0 0 1 1 X+1 1 0 1 1 X X 1 X+1 0 0 X X 0 0 X X X+1 0 1 X+1 1 0 0 X X+1 0 X+1 X 1 1 1 X
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X 0 X X 0 0 0 X X X X X X 0 X X X X X X 0 X X 0 X 0 X 0 X 0 0 0 X 0 X 0 0 X 0 X X 0 0 0 X X 0 X 0 X X 0 X 0 0 X X X X 0 X X 0 0 0 0 X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X 0 X 0 0 X X 0 X X X 0 X X X 0 0 X 0 0 X 0 X 0 X 0 X 0 X X X X X X 0 0 X 0 X 0 X 0 0 0 0 X 0 X X 0 X X 0 X X 0 0 X 0 X X X 0 X 0 0 0 0 X X X X
0 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 0 0 0 0 X X X X X X X X X X X X X X X X X X 0 X X X X X X 0 X 0 0 X X X 0 X X 0 X X X 0 X X X X X X 0 0 0 0 X 0 X 0 0 X 0 0 X
generates a code of length 96 over Z2[X]/(X^2) who´s minimum homogenous weight is 83.
Homogenous weight enumerator: w(x)=1x^0+54x^83+139x^84+208x^85+212x^86+274x^87+372x^88+374x^89+394x^90+404x^91+417x^92+384x^93+411x^94+390x^95+417x^96+404x^97+354x^98+392x^99+379x^100+352x^101+258x^102+316x^103+268x^104+228x^105+190x^106+154x^107+147x^108+86x^109+79x^110+52x^111+30x^112+10x^113+14x^114+12x^115+6x^116+2x^117+8x^118
The gray image is a linear code over GF(2) with n=192, k=13 and d=83.
This code was found by Heurico 1.16 in 16.9 seconds.