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

generates a code of length 82 over Z5[X]/(X^2) who´s minimum homogenous weight is 316.

Homogenous weight enumerator: w(x)=1x^0+440x^316+160x^317+300x^318+600x^319+972x^320+1760x^321+420x^322+660x^323+700x^324+1064x^325+1360x^326+320x^327+300x^328+360x^329+620x^330+960x^331+320x^332+380x^333+420x^334+476x^335+580x^336+120x^337+200x^338+280x^339+332x^340+680x^341+160x^342+160x^343+140x^344+156x^345+220x^346+4x^350

The gray image is a linear code over GF(5) with n=410, k=6 and d=316.
This code was found by Heurico 1.16 in 0.54 seconds.