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

generates a code of length 99 over Z2[X]/(X^4) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+56x^100+5x^104+2x^108

The gray image is a linear code over GF(2) with n=792, k=6 and d=400.
This code was found by Heurico 1.16 in 0.75 seconds.