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

generates a code of length 83 over Z5[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+1364x^320+400x^322+360x^323+2532x^325+560x^327+420x^328+1904x^330+420x^332+1080x^333+1880x^335+880x^337+640x^338+1512x^340+240x^342+1224x^345+164x^350+8x^355+8x^360+4x^365+8x^370+4x^375+4x^380+8x^385

The gray image is a linear code over GF(5) with n=415, k=6 and d=320.
This code was found by Heurico 1.16 in 33.5 seconds.