The generator matrix

 1  0  0  0  0  1  1  1  1  0  1  1  X  1  0  X  X  1  X  1  X  0  1  X  1  1  1  1  0  0  1  0  1  1  0  0  1  1  0  1  1  0  X  0  X  1  1  X  X  1  0  X  1  1  1  1  1  1  1  1  1  1  0  0  1  1  X  1  1  X  1  1  1  1  X  1  0  1  1  X  1  0  X  X  0  0  1  1  1  1  1  0  0  1  0  X  0  0
 0  1  0  0  0  0  0  0  0  X  0  0  X  X  X  X  1  1  1  1  1  1 X+1  1 X+1 X+1  1 X+1  1  1  1  1  0  1  1  0  0  1  1  X  1  1  1  X  1  X X+1  1  1  0  1  0  1  X  0  X  1  0  0  X  1  1  X  0 X+1  X  1 X+1  X  X X+1  1 X+1  1  X  1  1  1  X  X  0  0  1  0  X  1  0  X X+1 X+1  0  0  0  0  0  0  0  1
 0  0  1  0  0  0  1  X  0  0  1 X+1  1 X+1  1  1  X  1 X+1 X+1  0  X  0 X+1 X+1  X  X  0  1  1  1  0  X  0 X+1  0 X+1  1  0  X  1 X+1 X+1  0 X+1  X  0  0  X X+1  1  1 X+1  X  X X+1  X  1  0 X+1  1  X  1  1  1  0  X  X  1  1  0  1  1  X  X  X  X  0  0  1  X  X  0  1  X  0  1  X  X  0 X+1  X  X  0  1  0  0 X+1
 0  0  0  1  0  1  1  1  X  1  X  X  X X+1 X+1  1  1  0  X X+1 X+1  0  1 X+1 X+1  0 X+1  X  0  1  0  0 X+1  1  X  1  0  X  X  0 X+1 X+1  X  1  X  X  X  1  X  X  X X+1  1 X+1  0  0  1 X+1  1  X  0  0 X+1  1 X+1  0  1  X  1  1  1 X+1  X  X  X X+1  0  X  1  0 X+1  1 X+1  0  X  X  1  1  X  X  1  1  1  1  X  1  1  1
 0  0  0  0  1  1  0  0  1  1  X X+1  1  1  X  1 X+1 X+1  1  0  X X+1 X+1  X X+1 X+1  X  0  X  1  0  0  1  0 X+1  1  1 X+1 X+1  0  1  X  X  0  0  X X+1  1 X+1  0 X+1  X  1  X X+1 X+1  X X+1  0 X+1 X+1  1  0  0  X  X  0  X  0  1  1  0 X+1  0  1  1  1  0  0  1  0 X+1  0 X+1  1  X  X X+1 X+1 X+1  X X+1  0  X  X  0  0  1
 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  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  X  X  0  0  0  X  X  0  X  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  X  0  X  X  0  X  0  0  X  X
 0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  0  X  X  0  0  0  X  0  0  X  X  X  0  X  0  0  X  X  0  X  0  X  X  X  0  X  0  X  X  0  X  0  X  0  X  X  X  X  X  X  0  X  0  0  X  X  0  X  X  X  0  X  0  0  X  X  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  0  0  0  X  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+66x^87+140x^88+176x^89+213x^90+236x^91+186x^92+224x^93+218x^94+192x^95+239x^96+210x^97+231x^98+210x^99+175x^100+158x^101+159x^102+150x^103+146x^104+122x^105+105x^106+102x^107+96x^108+94x^109+62x^110+38x^111+28x^112+36x^113+31x^114+28x^115+7x^116+4x^117+1x^118+2x^119+6x^120+4x^122

The gray image is a linear code over GF(2) with n=196, k=12 and d=87.
This code was found by Heurico 1.16 in 8.17 seconds.