The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1  0  1  1  1  1  1  X  1  1  0  1  1 X^2  1  1  X  1  0  1  0  1  0  X  1  1  1 X^2  1  1  X X^2  1  1  1  1  1  X  1 X^2  1  X  1  0  X  1  X  X  X  1  1 X^2  X  X
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2  0  X X^2+X  0  0 X^2+X X^2+X X^2 X^2+X  X X^2 X^2  X  X  0 X^2+X  0 X^2  X X^2  X  X  0  X X^2 X^2+X  0  X  0 X^2 X^2  0  X X^2+X  0  X  0  X X^2 X^2+X  X  X X^2 X^2  0 X^2 X^2+X  X X^2+X  X X^2+X X^2+X X^2  X  X X^2+X  0  0  X X^2+X X^2+X  X  X X^2+X  0 X^2  X X^2+X X^2+X X^2+X  X X^2+X X^2  X X^2+X X^2  0 X^2+X  X  X  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2 X^2+X  X  0  X X^2 X^2+X  0 X^2  X X^2  X X^2  0  X X^2+X X^2 X^2+X  0  X  X  X X^2  0 X^2+X  0  0 X^2  X X^2  0  X X^2 X^2+X X^2 X^2 X^2 X^2+X  X X^2+X  0  X X^2  X X^2+X X^2+X  X  X  X X^2  0 X^2 X^2  0  X  X  X X^2  X X^2+X X^2+X  X  0 X^2+X  0 X^2+X  X X^2+X  X  X  X  X X^2  X  0 X^2 X^2  0  X X^2+X X^2+X  X X^2+X  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+101x^88+4x^89+201x^90+44x^91+280x^92+96x^93+420x^94+160x^95+440x^96+208x^97+413x^98+200x^99+392x^100+184x^101+270x^102+96x^103+187x^104+12x^105+141x^106+12x^107+90x^108+8x^109+66x^110+29x^112+21x^114+13x^116+4x^118+2x^120+1x^148

The gray image is a linear code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 2.8 seconds.