The generator matrix

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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 228.

Homogenous weight enumerator: w(x)=1x^0+880x^228+1060x^229+1048x^230+1060x^231+2820x^232+4460x^233+5580x^234+4160x^235+3620x^236+7760x^237+9480x^238+12460x^239+9604x^240+5940x^241+12600x^242+17120x^243+21300x^244+16040x^245+10620x^246+20380x^247+23360x^248+29700x^249+20236x^250+11000x^251+22560x^252+23520x^253+24540x^254+15512x^255+8420x^256+11620x^257+11580x^258+9420x^259+3948x^260+1840x^261+2260x^262+2100x^263+940x^264+40x^265+8x^270+16x^275+8x^280+4x^290

The gray image is a linear code over GF(5) with n=310, k=8 and d=228.
This code was found by Heurico 1.16 in 218 seconds.