The generator matrix

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

generates a code of length 99 over Z2[X]/(X^4) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+104x^97+78x^98+204x^99+30x^100+36x^101+17x^102+36x^103+1x^104+4x^113+1x^126

The gray image is a linear code over GF(2) with n=792, k=9 and d=388.
This code was found by Heurico 1.16 in 1.22 seconds.