The generator matrix

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

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+186x^88+192x^89+656x^90+440x^91+759x^92+588x^93+771x^94+440x^95+780x^96+472x^97+677x^98+300x^99+475x^100+296x^101+329x^102+184x^103+231x^104+108x^105+119x^106+36x^107+77x^108+4x^109+36x^110+8x^111+13x^112+4x^113+4x^114+5x^116+1x^120

The gray image is a linear code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.16 in 5.93 seconds.