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  X X^3  X X^2  X X^3  X X^2  X  0  X X^3  X X^3+X^2  X X^2  X X^3  X X^3+X^2  X X^3+X^2  X  0  0  X  0  X X^2  X  0  X  0 X^3 X^2
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X  0 X^3+X^2+X X^2  X X^3+X^2  X  0 X^2+X  0 X^3+X^2+X X^2  X X^3+X^2  X  0 X^2+X  0 X^3+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^2 X^3+X X^2 X^3+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^3+X^2+X X^2 X^3+X X^3 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X X^3 X^2+X X^3+X^2 X^3+X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^3+X^2+X  X X^2+X  X  X  X X^3+X  X X^2+X  X  X  X X^2+X  X X^3+X^2+X  0  X  X  X X^3+X^2+X  X X^3+X  0 X^3+X^2+X  X  X  0
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3  0  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2  0  0 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2  0  0  0  0 X^3+X^2 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^2 X^3+X^2  0  0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3  0 X^2 X^2  0 X^3 X^3 X^2 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3  0
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  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  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 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  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3  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+216x^96+320x^98+312x^100+128x^102+12x^104+32x^106+3x^128

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 1.7 seconds.