The generator matrix

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

generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+68x^89+112x^90+132x^91+159x^92+164x^93+131x^94+132x^95+127x^96+88x^97+123x^98+92x^99+74x^100+90x^101+76x^102+72x^103+58x^104+46x^105+41x^106+40x^107+35x^108+24x^109+36x^110+32x^111+18x^112+20x^113+20x^114+8x^115+8x^116+10x^117+5x^118+4x^119+2x^121

The gray image is a linear code over GF(2) with n=196, k=11 and d=89.
This code was found by Heurico 1.10 in 4.47 seconds.