The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  X X^2+X  0  1  X  X X^2  1  1  1  X  1 X^2+X  1  X  1  1 X^2  X X^2 X^2+X X^2  1  1 X^2  0  1  1 X^2+X  1  1  1 X^2  1 X^2  1 X^2  1  1  0  0  1  X  0  1  1  0  1 X^2 X^2+X  0  1  X  X  1  1  1  0  1  1  1  1  X X^2+X  0  1  1  0  1  X  0  1  1 X^2  1  1  1  0  1 X^2+X  0  1  1
 0  1  0  0  0  0  0  0 X^2  1  1 X^2+1  1  1  1  1 X^2+X X^2+X  1  X  X X^2+X+1  1 X^2+X  1  1 X+1  1  0 X^2 X^2+X  X  1 X^2  1 X^2+1  0 X^2+X  1 X^2+1 X^2+X+1  1 X^2+X+1 X^2+X+1 X^2+1 X^2+X X^2+1  1  0 X^2 X^2+X X^2+X+1  1  1  0  1  1 X^2+X X^2+1  X  X  1 X^2 X^2 X^2+1 X^2+X  1 X^2 X^2+1 X^2+X+1  1 X+1  X X^2+X  X  1 X^2+X  X X+1 X^2+X+1  0  0  1 X^2  1 X^2 X^2 X^2 X^2+X  X X^2+X  X  1 X^2+X  X  0
 0  0  1  0  0  0  1  1  1  1 X^2+1 X^2  X X^2+1 X^2+1 X^2 X^2  0 X^2+X+1  1  1 X+1 X^2+X  1 X^2+X+1 X^2+1 X^2  X  X X^2+X+1  1  1  X  0  X  0  X X^2 X^2+X+1 X^2+1 X^2+1 X+1 X^2+X+1 X^2+X  X  0 X^2+1 X^2+X  X  1 X^2+1  0  0  0 X^2+X+1  1 X+1 X^2+X+1  0  1 X^2+X+1 X+1  1  1 X^2  0 X^2+1  X X^2+X  1 X^2 X^2+1 X^2+X X^2+X+1  0 X^2+X+1 X^2+X X^2+X  X X^2+X  1 X^2+X+1  0  1  1 X^2+X+1  1  X  0 X^2+1 X^2 X^2+X+1 X^2+X  0  0  0
 0  0  0  1  0  1  1 X^2 X^2+1 X^2 X^2+1  1 X^2 X+1 X^2+X X+1 X+1  1 X^2  X  X X^2 X+1 X^2+1 X+1 X^2+1  0 X^2+X+1 X^2+X  1  X X^2+X  1  1  0  1  X X^2 X^2 X^2+X X+1 X^2+1 X^2+X  1  X  1 X^2+X+1  1  1  1 X+1 X^2+X+1 X^2 X^2+X+1 X^2  1  X  0  0 X+1  1 X+1 X^2 X^2 X^2+1  1 X^2+X X+1 X+1 X+1  X X^2 X^2+X+1  1  X X+1  1  1 X^2  X X^2+1  1 X+1 X+1 X^2+X  X X^2+X+1  1 X^2  X  1  X X^2  1 X^2+X+1  0
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  0  1  0 X+1 X^2 X^2+1 X^2+X+1  0 X^2+1  0 X^2+1 X^2 X^2+X+1 X^2+1  X  X X+1 X^2+X X^2+X  1 X^2+1 X^2+X X+1 X+1 X+1 X^2+1 X+1  0  1  0 X^2+X+1  1 X^2  X X^2+X  0 X^2+X X^2+X  0 X^2  X X^2 X+1 X^2+X  1 X^2+X X^2+1 X^2+X+1 X^2  1 X^2+1 X^2+X X+1  1 X^2+X+1  X X^2+X+1  0 X^2+1 X+1 X^2+X X^2 X^2 X^2+X X^2+1 X^2+X X+1 X+1  0 X^2+X X+1 X^2 X^2+X+1  X  0  X X^2+1  1 X+1 X^2+X+1 X+1 X^2+X X^2+X+1 X^2+1 X^2+X+1 X^2+X+1  0
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 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  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 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+76x^84+486x^85+815x^86+1306x^87+1540x^88+2652x^89+2292x^90+3690x^91+3390x^92+4824x^93+4088x^94+5604x^95+4416x^96+5338x^97+4155x^98+5004x^99+3251x^100+3774x^101+2342x^102+2298x^103+1371x^104+1214x^105+539x^106+474x^107+245x^108+138x^109+89x^110+56x^111+44x^112+4x^113+10x^114+2x^116+2x^117+6x^118

The gray image is a linear code over GF(2) with n=384, k=16 and d=168.
This code was found by Heurico 1.13 in 81.4 seconds.