The generator matrix

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

generates a code of length 61 over Z5[X]/(X^2) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+860x^224+848x^225+600x^226+1320x^227+2640x^228+5100x^229+5472x^230+3000x^231+5000x^232+6340x^233+11820x^234+11256x^235+6300x^236+8780x^237+12540x^238+19680x^239+21056x^240+10800x^241+14420x^242+17900x^243+28720x^244+28548x^245+13800x^246+16660x^247+20260x^248+27900x^249+24280x^250+10200x^251+11380x^252+11080x^253+13600x^254+8580x^255+2800x^256+2440x^257+1740x^258+2320x^259+536x^260+20x^265+8x^270+12x^275+4x^280+4x^285

The gray image is a linear code over GF(5) with n=305, k=8 and d=224.
This code was found by Heurico 1.16 in 214 seconds.