The generator matrix

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

generates a code of length 97 over Z2[X]/(X^2) who�s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+121x^88+256x^90+332x^92+242x^94+228x^96+204x^98+153x^100+128x^102+105x^104+82x^106+55x^108+46x^110+46x^112+22x^114+12x^116+12x^118+3x^120

The gray image is a linear code over GF(2) with n=194, k=11 and d=88.
This code was found by Heurico 1.16 in 1.03 seconds.