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

generates a code of length 96 over Z5[X]/(X^2) who´s minimum homogenous weight is 375.

Homogenous weight enumerator: w(x)=1x^0+124x^375+776x^380+2100x^385+16x^390+4x^395+64x^400+12x^405+8x^410+12x^415+4x^420+4x^475

The gray image is a linear code over GF(5) with n=480, k=5 and d=375.
This code was found by Heurico 1.16 in 0.207 seconds.