The generator matrix

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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 298.

Homogenous weight enumerator: w(x)=1x^0+640x^298+1160x^299+528x^300+500x^301+2880x^302+4300x^303+5920x^304+3124x^305+2040x^306+6260x^307+8800x^308+10620x^309+6656x^310+4060x^311+10900x^312+15940x^313+19940x^314+10692x^315+5520x^316+15660x^317+21920x^318+26440x^319+14120x^320+6940x^321+19420x^322+25840x^323+27540x^324+12552x^325+6960x^326+15500x^327+18640x^328+18940x^329+8576x^330+3140x^331+7880x^332+7800x^333+6100x^334+1744x^335+840x^336+1500x^337+1120x^338+840x^339+96x^340+8x^345+12x^350+8x^355+8x^360

The gray image is a linear code over GF(5) with n=400, k=8 and d=298.
This code was found by Heurico 1.16 in 323 seconds.