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

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+318x^96+256x^97+320x^98+512x^99+128x^100+256x^101+64x^102+192x^104+1x^192

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 111 seconds.