The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+90x^89+315x^90+242x^91+414x^92+294x^93+484x^94+266x^95+424x^96+182x^97+311x^98+152x^99+264x^100+122x^101+138x^102+94x^103+83x^104+44x^105+74x^106+22x^107+28x^108+16x^109+18x^110+4x^111+2x^112+2x^114+4x^115+2x^118+4x^121

The gray image is a linear code over GF(2) with n=384, k=12 and d=178.
This code was found by Heurico 1.16 in 1.76 seconds.