The generator matrix

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

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+142x^89+161x^90+438x^91+275x^92+440x^93+306x^94+408x^95+275x^96+356x^97+175x^98+272x^99+101x^100+222x^101+92x^102+98x^103+71x^104+100x^105+50x^106+48x^107+12x^108+18x^109+13x^110+14x^111+1x^112+2x^113+2x^114+2x^115+1x^118

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 1.59 seconds.