The generator matrix

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

generates a code of length 84 over Z5[X]/(X^2) who´s minimum homogenous weight is 324.

Homogenous weight enumerator: w(x)=1x^0+620x^324+1228x^325+640x^327+1040x^329+1868x^330+420x^332+1160x^334+1636x^335+400x^337+680x^339+1472x^340+880x^342+900x^344+1424x^345+160x^347+600x^349+452x^350+12x^355+8x^365+4x^375+4x^380+8x^385+4x^390+4x^400

The gray image is a linear code over GF(5) with n=420, k=6 and d=324.
This code was found by Heurico 1.16 in 24.6 seconds.