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  X  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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X X^2  X  X  X  X  X  X  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^2  0  0  0  0 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3+X^2  0 X^2  0  0  0 X^3  0 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3  0 X^3 X^2 X^3+X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^2 X^2 X^2 X^2  0 X^3  0 X^3 X^2 X^2 X^2 X^2  0 X^3 X^2  0 X^2 X^3 X^2  0 X^3 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0  0  0  0 X^3 X^3 X^3 X^3
 0  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^2 X^3+X^2  0 X^3  0  0 X^2 X^2 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2  0  0 X^2 X^2 X^3  0 X^2 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3  0 X^3+X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^3+X^2 X^3 X^3+X^2  0 X^3  0 X^3 X^3  0  0  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+238x^96+512x^99+158x^100+112x^104+1x^128+2x^132

The gray image is a linear code over GF(2) with n=792, k=10 and d=384.
This code was found by Heurico 1.16 in 0.953 seconds.