The generator matrix

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

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+128x^86+346x^88+442x^90+434x^92+430x^94+453x^96+376x^98+328x^100+300x^102+274x^104+206x^106+138x^108+130x^110+62x^112+32x^114+12x^116+4x^118

The gray image is a linear code over GF(2) with n=194, k=12 and d=86.
This code was found by Heurico 1.10 in 1.31 seconds.