The generator matrix

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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 309.

Homogenous weight enumerator: w(x)=1x^0+100x^309+1128x^310+1160x^311+760x^312+560x^313+320x^314+1512x^315+1180x^316+340x^317+340x^318+220x^319+1400x^320+1220x^321+280x^322+260x^323+160x^324+848x^325+660x^326+280x^327+140x^328+40x^329+728x^330+500x^331+240x^332+180x^333+160x^334+504x^335+280x^336+100x^337+20x^338+4x^340

The gray image is a linear code over GF(5) with n=400, k=6 and d=309.
This code was found by Heurico 1.16 in 1.39 seconds.