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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 312.

Homogenous weight enumerator: w(x)=1x^0+360x^312+380x^313+220x^314+588x^315+800x^316+1560x^317+900x^318+440x^319+780x^320+660x^321+1360x^322+940x^323+340x^324+440x^325+380x^326+780x^327+540x^328+200x^329+352x^330+220x^331+800x^332+400x^333+220x^334+248x^335+280x^336+460x^337+340x^338+80x^339+216x^340+160x^341+180x^342

The gray image is a linear code over GF(5) with n=405, k=6 and d=312.
This code was found by Heurico 1.16 in 0.531 seconds.