The generator matrix

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

generates a code of length 97 over Z2[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+120x^86+318x^88+451x^90+488x^92+450x^94+402x^96+373x^98+370x^100+283x^102+239x^104+211x^106+158x^108+118x^110+55x^112+37x^114+16x^116+5x^118+1x^120

The gray image is a linear code over GF(2) with n=194, k=12 and d=86.
This code was found by Heurico 1.16 in 4.11 seconds.