The generator matrix

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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 295.

Homogenous weight enumerator: w(x)=1x^0+104x^295+100x^299+564x^300+280x^301+20x^302+1740x^304+888x^305+860x^306+540x^307+3840x^309+2192x^310+1560x^311+1140x^312+5440x^314+2268x^315+2380x^316+3640x^317+8740x^319+3120x^320+2880x^321+4540x^322+10540x^324+3428x^325+2700x^326+2620x^327+5600x^329+1928x^330+1520x^331+1500x^334+620x^335+320x^336+160x^340+104x^345+84x^350+60x^355+48x^360+32x^365+12x^370+8x^375+4x^380

The gray image is a linear code over GF(5) with n=400, k=7 and d=295.
This code was found by Heurico 1.16 in 14.6 seconds.