The generator matrix

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

generates a code of length 84 over Z5[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+868x^320+2520x^321+780x^322+240x^324+2628x^325+6860x^326+1600x^327+560x^329+4056x^330+8180x^331+2020x^332+500x^334+4312x^335+9440x^336+2000x^337+540x^339+3888x^340+9180x^341+2080x^342+480x^344+2824x^345+6400x^346+1080x^347+180x^349+1708x^350+2200x^351+440x^352+304x^355+220x^356+8x^360+12x^365+8x^370+8x^375

The gray image is a linear code over GF(5) with n=420, k=7 and d=320.
This code was found by Heurico 1.16 in 13.1 seconds.