The generator matrix

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

generates a code of length 93 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+30x^81+81x^82+112x^83+171x^84+156x^85+177x^86+216x^87+246x^88+224x^89+210x^90+210x^91+197x^92+238x^93+218x^94+206x^95+192x^96+194x^97+171x^98+144x^99+108x^100+124x^101+97x^102+96x^103+67x^104+48x^105+49x^106+30x^107+25x^108+10x^109+8x^110+10x^111+11x^112+8x^114+3x^116+4x^118+3x^120+1x^122

The gray image is a linear code over GF(2) with n=186, k=12 and d=81.
This code was found by Heurico 1.16 in 4.32 seconds.