The generator matrix

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

generates a code of length 86 over Z5[X]/(X^2) who´s minimum homogenous weight is 322.

Homogenous weight enumerator: w(x)=1x^0+500x^322+1340x^323+1540x^324+1244x^325+1920x^326+3480x^327+5240x^328+6220x^329+4304x^330+5000x^331+7600x^332+9540x^333+10860x^334+7756x^335+7720x^336+12340x^337+15060x^338+16480x^339+11364x^340+10800x^341+17440x^342+20140x^343+20800x^344+14284x^345+13900x^346+17940x^347+21120x^348+20680x^349+12976x^350+11680x^351+15460x^352+15440x^353+13420x^354+6616x^355+5200x^356+6840x^357+6260x^358+4500x^359+1916x^360+1280x^361+900x^362+860x^363+500x^364+128x^365+8x^370+12x^375+12x^380+4x^400

The gray image is a linear code over GF(5) with n=430, k=8 and d=322.
This code was found by Heurico 1.16 in 352 seconds.