The generator matrix

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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 319.

Homogenous weight enumerator: w(x)=1x^0+940x^319+300x^320+1020x^324+200x^325+300x^329+36x^330+80x^334+80x^335+160x^339+4x^350+4x^355

The gray image is a linear code over GF(5) with n=405, k=5 and d=319.
This code was found by Heurico 1.16 in 77.8 seconds.