The generator matrix

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

generates a code of length 82 over Z5[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+152x^320+60x^321+220x^324+1192x^325+320x^326+240x^329+364x^330+20x^331+168x^335+60x^336+212x^340+40x^341+40x^344+24x^345+12x^350

The gray image is a linear code over GF(5) with n=410, k=5 and d=320.
This code was found by Heurico 1.16 in 0.103 seconds.