The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+66x^88+186x^89+238x^90+288x^91+297x^92+290x^93+340x^94+314x^95+269x^96+246x^97+280x^98+318x^99+279x^100+204x^101+158x^102+138x^103+63x^104+24x^105+25x^106+20x^107+8x^108+6x^109+6x^110+8x^111+8x^112+4x^113+3x^114+2x^115+4x^118+1x^122+1x^128+1x^130

The gray image is a linear code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 2 seconds.