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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 305.

Homogenous weight enumerator: w(x)=1x^0+448x^305+1160x^306+940x^307+320x^308+220x^309+1248x^310+1520x^311+720x^312+220x^313+400x^314+668x^315+1200x^316+800x^317+180x^318+260x^319+748x^320+900x^321+420x^322+140x^323+20x^324+752x^325+720x^326+380x^327+100x^328+80x^329+260x^330+500x^331+240x^332+40x^333+20x^334

The gray image is a linear code over GF(5) with n=395, k=6 and d=305.
This code was found by Heurico 1.16 in 0.578 seconds.