The generator matrix

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

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+67x^86+165x^88+203x^90+213x^92+196x^94+209x^96+225x^98+180x^100+192x^102+181x^104+104x^106+47x^108+17x^110+16x^112+9x^114+5x^116+7x^118+4x^120+3x^122+1x^124+1x^126+1x^132+1x^140

The gray image is a linear code over GF(2) with n=194, k=11 and d=86.
This code was found by Heurico 1.16 in 1.34 seconds.