The generator matrix

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

generates a code of length 96 over Z5[X]/(X^2) who´s minimum homogenous weight is 361.

Homogenous weight enumerator: w(x)=1x^0+520x^361+860x^362+960x^363+1200x^364+2340x^365+4320x^366+4420x^367+3860x^368+4200x^369+5140x^370+10060x^371+9020x^372+6900x^373+6280x^374+8716x^375+13840x^376+13260x^377+11180x^378+9140x^379+12900x^380+18640x^381+18580x^382+13620x^383+11140x^384+15740x^385+22760x^386+20200x^387+14320x^388+11100x^389+14256x^390+19900x^391+15740x^392+11280x^393+8260x^394+8304x^395+10900x^396+8540x^397+4500x^398+3240x^399+2788x^400+3560x^401+1700x^402+880x^403+440x^404+408x^405+500x^406+180x^407+8x^410+12x^415+4x^420+8x^425

The gray image is a linear code over GF(5) with n=480, k=8 and d=361.
This code was found by Heurico 1.16 in 359 seconds.