The generator matrix

 1  0  1  1  1  X  1  1 X^3+X^2+X  1 X^3  1  1  1  1 X^2+X  1  1 X^3+X X^3+X^2+X  1  X  1  1 X^3+X^2 X^2  1  1 X^3  1  1  0 X^3+X^2+X  1  1  1  1  1  1  1  1  0  1  1 X^3+X X^2  1  1 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2+X  1  X  1  X  0 X^3+X  1  1 X^3+X^2 X^2+X  X X^2+X X^3+X^2+X  1  0 X^3+X^2  1  1  1 X^3  0 X^3+X^2  0 X^3  1 X^3+X^2+X  1  X  1 X^3+X  1  1  X X^3+X  X  1 X^3+X^2  1  1  1  X  1  1  1 X^3+X
 0  1  1 X^2 X+1  1  X X^2+X+1  1  X  1 X^2+X+1 X+1 X^2+1 X^3  1  1 X^3+X^2  1  1  X  1  X X^2+1  1  1 X^3+X+1 X^2  1 X^3+X^2+X+1  0  1  1 X^3+X^2+X X^3+X^2+1 X^2 X^2+X+1 X^3 X^2+1 X^3+1 X^3+X^2+X  1 X^2+X X+1  1  1  1 X^2+X  1  1  1  1  1  1 X^2+X+1  1 X^2+X  1  1  1 X^2+X X^3+X^2+X+1  1  1  1  1  1 X^3  X  1 X^2+1 X^3+X^2 X^3+X^2+1  X X^3+X^2  1  1  1 X+1  1 X^2+X+1  1 X^2+1  1  0 X^2+X  1  1 X^3+X^2 X^3+X^2  1 X^3+X  X X^3+X^2+1 X^3  1 X^3+X^2+X X^3+X^2+1  1
 0  0  X X^3+X X^3 X^3+X X^3+X  X X^3+X^2 X^2 X^3+X X^3+X^2 X^2+X X^2+X X^2 X^3 X^3+X^2 X^2+X X^2+X X^3+X  0 X^2 X^2+X X^3  0  X X^3+X^2 X^2 X^2  0 X^3+X^2+X X^2+X X^3+X^2+X  X X^3+X X^3 X^3+X^2+X X^3+X X^2 X^2+X X^3+X^2 X^3+X X^2+X  X  0 X^2 X^3  0 X^3+X^2+X X^3+X^2+X X^3+X X^2+X X^3 X^3  0 X^2+X  X X^3+X^2 X^2 X^3+X X^3+X^2 X^3+X^2+X X^3 X^3+X^2+X  0 X^3+X X^2 X^3+X^2+X X^3+X^2 X^2 X^3+X X^3 X^2  0  X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2+X  X X^3+X X^3  0 X^2 X^3 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X X^3+X^2+X X^3  X X^3 X^3 X^2 X^3 X^2+X  0

generates a code of length 99 over Z2[X]/(X^4) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+384x^96+184x^97+500x^98+176x^99+336x^100+160x^101+152x^102+48x^103+67x^104+8x^105+8x^106+6x^108+4x^110+12x^116+2x^136

The gray image is a linear code over GF(2) with n=792, k=11 and d=384.
This code was found by Heurico 1.16 in 79.1 seconds.