The generator matrix

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

generates a code of length 59 over Z5[X]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+448x^220+680x^221+720x^222+640x^223+100x^224+2540x^225+3780x^226+2500x^227+1540x^228+540x^229+4128x^230+4840x^231+3960x^232+2300x^233+580x^234+5628x^235+5640x^236+4220x^237+2760x^238+820x^239+6292x^240+6240x^241+4580x^242+2220x^243+460x^244+3464x^245+3260x^246+1520x^247+540x^248+556x^250+560x^251+28x^255+28x^260+4x^265+4x^270+4x^275

The gray image is a linear code over GF(5) with n=295, k=7 and d=220.
This code was found by Heurico 1.16 in 9.22 seconds.