The generator matrix

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

generates a code of length 98 over Z5[X]/(X^2) who´s minimum homogenous weight is 375.

Homogenous weight enumerator: w(x)=1x^0+1028x^375+1180x^376+1260x^377+400x^378+260x^379+3836x^380+2900x^381+3080x^382+680x^383+440x^384+4416x^385+4220x^386+4260x^387+1140x^388+600x^389+5720x^390+4720x^391+3560x^392+1080x^393+440x^394+5028x^395+3920x^396+3680x^397+920x^398+380x^399+4148x^400+3140x^401+2240x^402+560x^403+260x^404+2860x^405+1820x^406+1640x^407+220x^408+120x^409+924x^410+600x^411+280x^412+136x^415+12x^420+4x^425+4x^430+4x^440+4x^450

The gray image is a linear code over GF(5) with n=490, k=7 and d=375.
This code was found by Heurico 1.16 in 15.7 seconds.