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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+113x^96+10x^100+1x^104+2x^108+1x^120

The gray image is a linear code over GF(2) with n=768, k=7 and d=384.
This code was found by Heurico 1.16 in 1.06 seconds.