The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 4X  1  1  1 3X  1  1  1  1  0  1  1  1 3X  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  X  1  1  1  1 2X  1  X  1 4X  1  1  1  1  1 3X  1 4X  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  0  1  1 3X  1  1  1  X  1  1 4X  1  1  1
 0  1  0 3X 2X  X  1 3X+2 3X+3 3X+1 2X+1 4X+1 3X+4  2 2X+4 X+3  3  1 X+4 4X+2  1 X+3 4X+3  0  1  4  2 2X+2  1  1 3X+4 2X+4 4X+1  1 4X+4 2X+3 3X+2 2X+3 4X+3 2X+2  2 2X+2 2X  1  1 3X+3  4 3X  1  1 2X+3 3X+2 2X+1 3X+1  1 X+4 4X 4X+1  1 X+1 4X+2  X X+1 3X+3  1 X+2  1  2 2X+1 4X+4 3X+2  1 X+3 3X+3 3X+4 X+3 2X+2  1 3X+1 X+2 X+4 2X+3  1 2X+1 4X+2  1 4X+3 2X+4  1  1 3X+2 2X+1  1 2X+3 4X+3 3X
 0  0  1 3X+1  2  4 X+4 3X+4 4X+4 3X+2 3X+3  X X+2 2X+2 3X X+1 4X+3  2  1  0  1 2X X+2 2X+3 X+3 X+4 2X+3 X+1 2X+4 3X 3X+1  3 2X+1 3X+4 2X 4X+1 4X+4  X 4X+4 3X 3X+3  1 3X+2 4X+2 X+3 2X+2 4X+2 3X+3 3X+2  4  3 4X+2 X+4 2X+1 X+1  3  1 2X 3X+3 3X 2X+4 4X+2 2X+2  X 3X+2  0 4X 3X+4  4 2X+3 4X+3  1 X+3 3X+4 2X+2 4X+1 3X+2 3X+3 4X+3 X+4 4X+2  4 3X+2 2X+3 4X+3  1  4 4X 2X+2 2X+3 2X  0  X 4X+3 2X  0

generates a code of length 96 over Z5[X]/(X^2) who´s minimum homogenous weight is 374.

Homogenous weight enumerator: w(x)=1x^0+2220x^374+772x^375+3880x^379+816x^380+2380x^384+500x^385+1440x^389+560x^390+1300x^394+300x^395+840x^399+68x^400+440x^404+104x^405+4x^425

The gray image is a linear code over GF(5) with n=480, k=6 and d=374.
This code was found by Heurico 1.16 in 0.695 seconds.