The generator matrix

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

generates a code of length 96 over Z5[X]/(X^2) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+172x^360+60x^363+760x^364+428x^365+560x^366+560x^368+3080x^369+452x^370+940x^371+1200x^373+5720x^374+356x^375+1620x^376+1980x^378+8400x^379+336x^380+2460x^381+2880x^383+11040x^384+280x^385+2860x^386+3320x^388+11980x^389+188x^390+2600x^391+2020x^393+7060x^394+172x^395+1220x^396+480x^398+1820x^399+192x^400+240x^401+140x^404+176x^405+92x^410+92x^415+68x^420+36x^425+44x^430+16x^435+12x^440+8x^445+4x^455

The gray image is a linear code over GF(5) with n=480, k=7 and d=360.
This code was found by Heurico 1.16 in 18.2 seconds.