The generator matrix

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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 219.

Homogenous weight enumerator: w(x)=1x^0+1060x^219+300x^220+720x^224+204x^225+380x^229+36x^230+340x^234+80x^235+4x^255

The gray image is a linear code over GF(5) with n=280, k=5 and d=219.
This code was found by Heurico 1.16 in 0.0344 seconds.