The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+47x^84+86x^85+186x^86+280x^87+376x^88+594x^89+658x^90+882x^91+1014x^92+1112x^93+1219x^94+1210x^95+1286x^96+1258x^97+1239x^98+1092x^99+968x^100+752x^101+618x^102+462x^103+290x^104+220x^105+120x^106+140x^107+82x^108+54x^109+47x^110+24x^111+23x^112+16x^113+4x^114+6x^115+9x^116+4x^117+2x^118+2x^122+1x^130

The gray image is a linear code over GF(2) with n=384, k=14 and d=168.
This code was found by Heurico 1.16 in 25.5 seconds.