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

generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+25x^88+28x^89+124x^90+128x^91+123x^92+220x^93+93x^94+352x^95+105x^96+534x^97+92x^98+624x^99+70x^100+526x^101+73x^102+316x^103+66x^104+180x^105+65x^106+70x^107+88x^108+36x^109+45x^110+36x^111+26x^112+10x^113+14x^114+8x^115+6x^116+2x^117+3x^118+1x^120+1x^122+2x^123+1x^124+1x^126+1x^158

The gray image is a linear code over GF(2) with n=396, k=12 and d=176.
This code was found by Heurico 1.16 in 2.83 seconds.