The generator matrix

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

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+388x^220+100x^221+180x^222+760x^224+2308x^225+440x^226+720x^227+720x^229+2540x^230+340x^231+340x^232+720x^234+1700x^235+360x^236+440x^237+560x^239+1516x^240+200x^241+320x^242+240x^244+644x^245+60x^246+24x^250+4x^255

The gray image is a linear code over GF(5) with n=290, k=6 and d=220.
This code was found by Heurico 1.16 in 0.345 seconds.