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

generates a code of length 98 over Z5[X]/(X^2) who´s minimum homogenous weight is 369.

Homogenous weight enumerator: w(x)=1x^0+740x^369+808x^370+1160x^371+1080x^372+2240x^373+4580x^374+4176x^375+4040x^376+3840x^377+5840x^378+9980x^379+7404x^380+7860x^381+6180x^382+10300x^383+15340x^384+11772x^385+12400x^386+7480x^387+13000x^388+21260x^389+15176x^390+14660x^391+10520x^392+15300x^393+23600x^394+16468x^395+16500x^396+9960x^397+15320x^398+20060x^399+12720x^400+12500x^401+7520x^402+9480x^403+12360x^404+6948x^405+5160x^406+3000x^407+3280x^408+4200x^409+2428x^410+700x^411+420x^412+240x^413+380x^414+184x^415+20x^416+24x^420+8x^425+4x^430+4x^455

The gray image is a linear code over GF(5) with n=490, k=8 and d=369.
This code was found by Heurico 1.16 in 367 seconds.