The generator matrix

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

generates a code of length 82 over Z5[X]/(X^2) who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+820x^306+1200x^307+900x^308+900x^309+2028x^310+3600x^311+6040x^312+3600x^313+2940x^314+5580x^315+8060x^316+11660x^317+7480x^318+6980x^319+9580x^320+14020x^321+18620x^322+11680x^323+10220x^324+13356x^325+18060x^326+24760x^327+15000x^328+13220x^329+16196x^330+20260x^331+26540x^332+14700x^333+11420x^334+13672x^335+16700x^336+18080x^337+8800x^338+5780x^339+6756x^340+7360x^341+7240x^342+2620x^343+1040x^344+884x^345+1120x^346+860x^347+220x^348+32x^350+28x^355+4x^360+8x^365

The gray image is a linear code over GF(5) with n=410, k=8 and d=306.
This code was found by Heurico 1.16 in 330 seconds.