The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+224x^91+214x^92+326x^93+173x^94+220x^95+114x^96+178x^97+96x^98+100x^99+72x^100+86x^101+44x^102+54x^103+18x^104+34x^105+21x^106+28x^107+12x^108+16x^109+1x^110+14x^111+1x^114+1x^120

The gray image is a linear code over GF(2) with n=384, k=11 and d=182.
This code was found by Heurico 1.16 in 40.6 seconds.