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 1 1 1 X 1 1 0 1 1 1 0 X 0 X 1 1 1 1 1 X 1 1 0 X X X 1 X 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 X 1 0 1 1 0 X 1 0 1 1 1 0 0 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 1 X 1 X X+1 0 1 X+1 X 1 X X X+1 0 X 1 1 0 1 X+1 1 1 1 0 X+1 X 1 0 0 0 0 1 0 1 0 1 0 X 1 0 1 1 X X+1 1 1 1 X 0 0 0 1 1 X 1 X+1 1 0 1 X 1 X 0 0 X X 0 X X 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 1 1 X X X+1 X+1 X+1 0 X X+1 1 X+1 X 1 0 X X+1 X 0 0 X X+1 X X 0 1 X 0 X 0 1 0 0 0 1 1 X+1 0 X+1 X+1 1 0 0 X+1 0 0 1 X 1 X+1 1 X+1 1 X 1 X+1 1 X 0 1 1 X 0 1 0 X+1 1 1 1 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 1 X 1 0 1 X+1 0 0 1 0 X+1 X 0 X+1 1 1 X+1 X+1 1 X+1 1 X X 1 X X+1 X 1 1 0 1 0 X+1 X+1 0 1 X X 0 1 X+1 X 1 0 1 X X X+1 X 1 X+1 X 1 X 1 X 1 1 X+1 0 0 0 0 X X+1 0 X X X 0
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 0 X+1 0 X+1 X X+1 X 1 X 0 0 X 0 X X X+1 1 0 0 X+1 0 1 1 1 1 X 1 1 X 0 X 1 1 X+1 X+1 0 X 0 X+1 X 0 X 1 1 1 1 0 X+1 X X 1 0 X 1 1 X+1 X X+1 0 0 1 1 1 X+1 1 X+1 X 1 X 1
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 0 0 0 X X 0 X X X 0 X 0 0 X 0 0 0 0 X X 0 0 X 0 X 0 X X X X 0 0 X 0 X 0 X X 0 0 X X X X X 0 X 0 0 0 X X 0 0 X X X 0 0 0 0 X X X X 0 0 0 X X
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 X X 0 0 0 X 0 0 X 0 0 0 0 X X X 0 X X X 0 0 0 0 X X X X X 0 0 0 0 X X 0 0 X 0 X X 0 0 0 X 0 X X 0 X X 0 X X 0 0 X X 0 X X 0 0 X 0 0 0 X 0
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 0 0 X X X X X X X X X X X X X X X X X X X 0 X X 0 X X X X X 0 X 0 X X 0 X X X 0 X X X 0 0 0 X X 0 0 X 0 X X 0 0 X X X X
generates a code of length 97 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+85x^84+144x^85+169x^86+250x^87+293x^88+306x^89+400x^90+388x^91+386x^92+418x^93+371x^94+436x^95+415x^96+370x^97+393x^98+380x^99+360x^100+376x^101+351x^102+336x^103+273x^104+252x^105+245x^106+186x^107+161x^108+152x^109+91x^110+58x^111+64x^112+24x^113+25x^114+14x^115+7x^116+6x^117+2x^118+2x^120+1x^122+1x^124
The gray image is a linear code over GF(2) with n=194, k=13 and d=84.
This code was found by Heurico 1.16 in 20.9 seconds.