The generator matrix

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

generates a code of length 86 over Z5[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+144x^320+364x^325+456x^330+100x^332+432x^335+1200x^337+336x^340+4800x^342+296x^345+6400x^347+228x^350+156x^355+200x^360+136x^365+144x^370+60x^375+68x^380+48x^385+24x^390+16x^395+12x^400+4x^415

The gray image is a linear code over GF(5) with n=430, k=6 and d=320.
This code was found by Heurico 1.16 in 1.57 seconds.