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 X^2  0  1  1  1  1  1  1  1  1  1  1  1 X^2  1  0  1  X  1  X  1  1  X  1  1  1  1  1 X^2  1  1  X  X  1  X  1  1  1  1  X  X  1  1  X  1  1  1  1  X  1  1  0  0 X^2 X^2  0  1 X^2  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2  0 X^2  X  X X^2+X X^2 X^2+X  X X^2  X  X X^2 X^2  0 X^2  X  X  X  X X^2+X  X  X X^2+X X^2 X^2  X X^2 X^2  X X^2 X^2 X^2 X^2+X X^2 X^2 X^2+X X^2+X  0 X^2+X  X  X  X X^2  X  X X^2+X  X X^2+X  X X^2 X^2 X^2 X^2+X X^2+X X^2 X^2 X^2  X X^2+X X^2+X X^2  X X^2 X^2 X^2 X^2+X  X  X  X X^2  X  X X^2  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X  X X^2+X X^2 X^2  0 X^2+X  X X^2+X  0  X  X X^2 X^2+X X^2  0  0 X^2  0  X  X X^2+X  0  0 X^2+X X^2+X X^2 X^2+X X^2+X  0  X  0 X^2+X X^2  0 X^2+X X^2 X^2+X  0 X^2  0 X^2+X X^2  0 X^2+X  0 X^2  0 X^2+X X^2  X X^2+X X^2 X^2+X X^2  X X^2+X X^2 X^2  X  X  0  X X^2+X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2+X  0  X X^2  X  X  0 X^2  X  0 X^2+X  X  X X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  X  X  0 X^2+X X^2  0 X^2  X X^2+X X^2 X^2  X  0  X X^2+X  0 X^2+X  0  X X^2+X X^2 X^2  0 X^2+X  0 X^2+X X^2+X X^2+X X^2  X X^2  X  X  X X^2+X X^2+X X^2 X^2+X  X  0  0 X^2+X  0  X  0  0 X^2+X  0 X^2+X  0 X^2  0  X X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 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 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 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 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 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 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  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+43x^88+80x^89+149x^90+146x^91+140x^92+184x^93+316x^94+320x^95+251x^96+366x^97+330x^98+338x^99+279x^100+250x^101+216x^102+128x^103+125x^104+98x^105+80x^106+60x^107+32x^108+34x^109+50x^110+22x^111+20x^112+8x^113+8x^114+8x^115+5x^116+4x^117+2x^118+2x^119+1x^154

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 2.66 seconds.