The generator matrix

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

generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+74x^87+130x^88+192x^89+199x^90+196x^91+269x^92+202x^93+210x^94+198x^95+238x^96+224x^97+165x^98+210x^99+178x^100+174x^101+131x^102+158x^103+166x^104+132x^105+110x^106+120x^107+112x^108+66x^109+46x^110+50x^111+41x^112+28x^113+27x^114+18x^115+16x^116+6x^117+5x^118+3x^122+1x^124

The gray image is a linear code over GF(2) with n=196, k=12 and d=87.
This code was found by Heurico 1.16 in 87.9 seconds.