The generator matrix

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

generates a code of length 61 over Z5[X]/(X^2) who´s minimum homogenous weight is 228.

Homogenous weight enumerator: w(x)=1x^0+680x^228+600x^229+624x^230+340x^231+1020x^232+3560x^233+1880x^234+2020x^235+880x^236+2500x^237+5880x^238+3180x^239+2528x^240+1140x^241+2720x^242+7760x^243+3320x^244+3600x^245+1100x^246+3540x^247+8640x^248+3560x^249+3092x^250+1160x^251+2160x^252+5040x^253+2200x^254+1156x^255+380x^256+560x^257+940x^258+260x^259+44x^260+20x^265+8x^270+20x^275+8x^280+4x^285

The gray image is a linear code over GF(5) with n=305, k=7 and d=228.
This code was found by Heurico 1.16 in 9.06 seconds.