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

generates a code of length 83 over Z5[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+512x^320+240x^321+260x^322+420x^323+600x^324+2336x^325+580x^326+700x^327+580x^328+520x^329+1616x^330+340x^331+340x^332+400x^333+320x^334+1172x^335+400x^336+300x^337+280x^338+280x^339+1016x^340+300x^341+280x^342+220x^343+200x^344+624x^345+100x^346+120x^347+100x^348+80x^349+344x^350+40x^351+4x^360

The gray image is a linear code over GF(5) with n=415, k=6 and d=320.
This code was found by Heurico 1.16 in 0.55 seconds.