The generator matrix

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

generates a code of length 97 over Z5[X]/(X^2) who´s minimum homogenous weight is 378.

Homogenous weight enumerator: w(x)=1x^0+2000x^378+1200x^379+204x^380+2800x^383+1420x^384+180x^385+1780x^388+920x^389+60x^390+1340x^393+600x^394+60x^395+1120x^398+440x^399+24x^400+620x^403+340x^404+76x^405+340x^408+80x^409+20x^410

The gray image is a linear code over GF(5) with n=485, k=6 and d=378.
This code was found by Heurico 1.16 in 12.4 seconds.