The generator matrix

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

generates a code of length 58 over Z5[X]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+88x^220+100x^224+184x^225+800x^229+132x^230+1600x^234+80x^235+56x^240+20x^245+16x^250+4x^255+20x^260+4x^265+12x^270+4x^275+4x^280

The gray image is a linear code over GF(5) with n=290, k=5 and d=220.
This code was found by Heurico 1.16 in 0.0608 seconds.