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

generates a code of length 97 over Z5[X]/(X^2) who´s minimum homogenous weight is 377.

Homogenous weight enumerator: w(x)=1x^0+800x^377+1600x^378+160x^380+2460x^382+2080x^383+132x^385+1500x^387+1100x^388+192x^390+1020x^392+1260x^393+60x^395+940x^397+620x^398+44x^400+460x^402+580x^403+20x^405+320x^407+260x^408+8x^410+8x^415

The gray image is a linear code over GF(5) with n=485, k=6 and d=377.
This code was found by Heurico 1.16 in 0.705 seconds.