The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 1 1 1 X 0 X X 0 0 1 1 1 1 1 X 1 1 1 X X 1 X 1 0 1 1 X 1 1 1 X 0 1 1 1 X 0 1 1 1 1 0 X X X 0 1 1 0 1 1 1 X X 1 1 1 0 0 X 1 1 0 X 1 X 1 1 X X 1 0 1 1 X 1 X 0 1 0 0
0 1 0 0 1 1 1 0 0 1 X+1 1 1 0 X X+1 X X+1 1 0 1 0 1 1 X X+1 0 1 1 1 X+1 0 X X 1 X 1 1 1 X+1 X 0 X X 1 0 1 0 1 X X 1 X+1 0 0 0 1 1 1 1 X X X 1 1 X+1 X 1 1 1 X+1 X+1 X 1 1 X X X 1 0 0 X X 1 1 X X 1 X+1 X 0 1 1 X+1 1 1
0 0 1 1 1 0 1 0 1 X+1 0 X X+1 1 1 X+1 0 X X 1 X+1 1 0 X+1 X+1 X 0 X+1 0 X+1 X+1 0 X+1 1 1 1 X 0 1 X+1 X+1 1 X 1 0 1 X 1 1 X+1 1 1 0 0 0 X+1 0 1 X X 1 X 1 X+1 1 1 0 X X X+1 0 0 1 0 X X 0 1 X X 1 X+1 1 X+1 X+1 X 1 X+1 X 1 X 1 1 1 0 0
0 0 0 X 0 0 0 0 0 X X 0 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 0 X X 0 0 0 X X 0 0 X X X 0 X X X 0 0 0 0 X X 0 X 0 0 0 0 X X X 0 X X X 0 X 0 X X X X X X X 0 0 X X 0 0 0 X X X X X X X X 0 X X 0 0
0 0 0 0 X 0 0 0 0 X 0 0 0 X 0 0 X X X X X X 0 X X 0 X 0 0 X 0 X 0 0 0 X X X X X X X 0 X X 0 0 0 0 0 X 0 0 0 X X X X 0 0 0 X X X X X X X 0 0 X 0 X X 0 0 X 0 X 0 0 0 X 0 X 0 X X 0 0 0 0 0 0 0 0
0 0 0 0 0 X 0 0 0 0 X 0 0 X 0 X X 0 X X X X 0 X X X 0 0 0 0 0 0 X X X 0 0 X 0 X 0 X 0 X 0 X X 0 0 X X X 0 X 0 0 X X X X 0 0 0 X X X X X X 0 0 X 0 X 0 0 0 0 0 0 0 X X X 0 X X X 0 0 0 0 X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X 0 0 0 0 X 0 0 0 X 0 X X X X X X X X X X X X X X 0 X X 0 0 X X X X X X 0 X X 0 X X X 0 X X 0 0 0 X 0 X X 0 0 0 X X 0 0 0 X 0 0 X X 0
0 0 0 0 0 0 0 X 0 0 0 X X X X X X X 0 0 0 X 0 X 0 0 X 0 X 0 X 0 X X 0 X 0 0 0 X 0 X 0 X X 0 X 0 X 0 0 X 0 0 0 0 0 0 X X 0 X X X X X X X 0 X X X 0 0 X X 0 0 0 0 0 X 0 X X 0 0 0 0 0 X 0 0 X 0 X
0 0 0 0 0 0 0 0 X X X 0 0 0 X 0 0 0 X 0 X X X X X 0 0 0 0 X 0 X X 0 0 X X X 0 X 0 0 X X 0 0 X X X X 0 0 X X 0 X 0 0 0 0 X 0 0 X X X 0 X X 0 X X X X 0 0 0 X 0 X 0 X 0 0 0 0 0 0 0 X X 0 X 0 0 X
generates a code of length 96 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+60x^84+56x^85+115x^86+148x^87+188x^88+204x^89+217x^90+238x^91+211x^92+222x^93+204x^94+208x^95+195x^96+206x^97+189x^98+184x^99+151x^100+188x^101+161x^102+156x^103+122x^104+96x^105+83x^106+70x^107+67x^108+46x^109+23x^110+16x^111+20x^112+6x^113+23x^114+4x^115+5x^116+8x^118+2x^120+2x^124+1x^126
The gray image is a linear code over GF(2) with n=192, k=12 and d=84.
This code was found by Heurico 1.16 in 4.44 seconds.