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

generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+60x^87+140x^88+186x^89+175x^90+226x^91+231x^92+228x^93+238x^94+222x^95+236x^96+198x^97+197x^98+190x^99+184x^100+182x^101+157x^102+124x^103+112x^104+114x^105+134x^106+124x^107+95x^108+64x^109+75x^110+56x^111+43x^112+38x^113+14x^114+20x^115+14x^116+14x^117+2x^118+2x^119

The gray image is a linear code over GF(2) with n=196, k=12 and d=87.
This code was found by Heurico 1.10 in 1.34 seconds.