The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 X X 0 X X X X X X 0 X 1 0 1 1 0 1 1 1 1 1 X 1 X 0 1 1 1 0 1 0 X 1 1 X 1 0 X 1 X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X 0 X 0 0 0 X X X 0 X X X 0 X X X X X X X X X 0 0 X X X X 0 X 0 X X X X 0 X X 0 X 0 0 X X 0 0 X 0 0 0 0 0 X X 0 0 0 0 X 0 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 0 X X X 0 X X 0 0 X X X 0 0 0 X 0 0 0 0 X X 0 X 0 0 X 0 X X X X X 0 0 X X 0 X 0 0 0 X X 0 0 0 X 0 X X 0 0 0 0 0 X X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 0 X X X 0 X 0 X X 0 X 0 0 X 0 X X X X 0 0 X X 0 0 0 0 0 0 X X X 0 X X 0 0 0 X X 0 0 0 0 0 X X 0 X 0 0 0 0 X X 0 0 X
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 X 0 0 0 0 X 0 X 0 0 X 0 0 0 X X X X X X X X X X X X X X 0 0 0 0 0 X X X X 0 0 0 0 X X 0 0 X 0 X X 0 X 0 X 0 X X
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 0 X X 0 X X X 0 X 0 0 0 X 0 0 X X 0 0 0 X 0 X X X X X 0 X 0 0 X X 0 0 0 X 0 X X X 0 0 0 0 0 X 0 X X 0 0 X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 0 X X X X 0 X X X X X X X X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 X X X X X X X 0 0 X X X 0 X X X X 0 X 0 0 X X 0 X X 0 X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X X X X X 0 0 0 0 X X X X 0 0 X X 0 X 0 0 0 X X 0 0 X 0 X 0 0 X X X 0 0 0 X X 0 X X 0 X X X 0 0 X X 0 0 0 0 X X 0 0 0 X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X X 0 0 0 X X X X 0 X 0 0 X X X 0 X 0 X 0 X 0 X X X 0 0 0 X 0 0 X X 0 X X 0 0 X 0 0 X 0 X X 0 X 0 0 X X 0 0 0 0 0 X 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 0 0 X 0 X X 0 X X 0 0 0 0 X X 0 0 X X X 0 X 0 X 0 X 0 X 0 X X 0 0 X 0 0 X 0 X 0 0 X X 0 X 0 X X X 0 X X X X X
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 X 0 0 X X X 0 0 0 X 0 0 0 X X X 0 X X 0 X 0 0 X 0 X 0 X 0 0 0 0 X X X 0 0 0 X X X X 0 X 0 0 X 0 0 0 0 X
generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.
Homogenous weight enumerator: w(x)=1x^0+40x^82+111x^84+6x^85+118x^86+38x^87+160x^88+96x^89+148x^90+116x^91+176x^92+162x^93+107x^94+286x^95+159x^96+320x^97+143x^98+296x^99+110x^100+282x^101+132x^102+210x^103+119x^104+128x^105+137x^106+68x^107+74x^108+30x^109+90x^110+10x^111+55x^112+68x^114+39x^116+30x^118+17x^120+7x^122+2x^124+3x^126+1x^128+1x^146
The gray image is a linear code over GF(2) with n=196, k=12 and d=82.
This code was found by Heurico 1.16 in 7.46 seconds.