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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+82x^92+160x^94+256x^95+104x^96+256x^97+68x^98+46x^100+24x^102+20x^104+4x^106+2x^120+1x^128

The gray image is a linear code over GF(2) with n=768, k=10 and d=368.
This code was found by Heurico 1.16 in 0.844 seconds.