The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1  1  X  1  1  1  1  1  1  1  1  1  1  0  1  1  1 2X  1  X  1  X  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1  1  1 4X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 4X  1  1  1 4X  1 2X  1 3X  1  0  1  1  1
 0  1  1  2  4  3 3X+1  0  2  1  3 3X+4  0 3X+1 3X+4  1  2  3  1  2 3X+4  0 3X+1  3 X+3 X+2  X 3X+4 3X+1  1  X 2X+2 2X+4  1 2X+4  1 4X+1  1 X+3  2 3X+4 3X X+1 2X+1 4X X+3  1 X+2 4X+1  X  1 2X+4  3 X+2 X+2  0 2X  1 3X+3 3X 3X+2 4X+4  X 2X+3  X 2X+1  X 3X+2 3X+1 X+2  1 2X  1 3X 4X  3  1 3X+1  1 4X  1  1  X 2X+3 2X+2  0
 0  0 3X  0  0  0  0  X 2X 3X 2X 3X 2X 4X  0 2X 2X 2X 2X 3X  X 2X  0 2X 2X 3X 3X  X  X 3X 4X 3X  0  X 4X  X 2X 2X 4X  0 3X  0  X 4X 4X 4X 2X 4X 2X 4X  X 2X 4X  0  0 2X  0  0  0 2X 3X  0 2X  0 2X 4X 4X 4X 4X 4X  0 2X 2X  X 3X 2X  X  X  0  0  X  X 4X 4X  X  0
 0  0  0  X  0  X 3X 3X  0 2X 2X 4X 2X 2X 3X  0 2X  X  X  X  0 4X 3X 4X  0 3X 3X  X 3X  0 3X  X 4X  X  X 2X 3X 3X  X 4X  0 2X 2X 2X 4X 4X 4X 3X 3X  0  0  0 4X  0 4X  X 4X 3X 2X 2X  0 4X  0 3X  X  X 3X 2X  X  0 4X 3X  0 4X  X 4X  X 2X 4X 2X 2X  X 4X 4X 3X  0
 0  0  0  0 3X 3X 2X 4X 4X  X 4X 4X 2X  0  0  0 3X 2X 3X 2X  X 2X  X  X  X  0 4X 4X  X  X 3X  X  X  X  X 2X  X 2X  0 4X 4X 4X 4X 3X 4X 2X  0 2X 3X 4X  X  0 3X 3X 3X  X  X 4X  X  X 2X 3X 3X  0 3X 4X  X 2X  0 3X  0  0 2X 3X 2X  0  0 3X  0 2X 4X  X 4X  0  X 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+164x^320+20x^322+280x^324+1212x^325+380x^327+1400x^329+3200x^330+940x^332+2740x^334+4608x^335+1980x^337+4520x^339+7524x^340+2680x^342+6020x^344+9420x^345+3560x^347+5540x^349+8356x^350+2300x^352+3720x^354+4456x^355+640x^357+780x^359+1072x^360+256x^365+80x^370+88x^375+80x^380+60x^385+20x^390+16x^395+8x^400+4x^405

The gray image is a linear code over GF(5) with n=430, k=7 and d=320.
This code was found by Heurico 1.16 in 16 seconds.