The generator matrix

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

generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+54x^88+215x^90+279x^92+258x^94+240x^96+202x^98+191x^100+167x^102+110x^104+101x^106+79x^108+49x^110+49x^112+25x^114+17x^116+5x^118+2x^120+2x^124+1x^126+1x^130

The gray image is a linear code over GF(2) with n=196, k=11 and d=88.
This code was found by Heurico 1.16 in 1.17 seconds.