The generator matrix

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

generates a code of length 60 over Z5[X]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+828x^220+760x^221+840x^222+880x^223+2440x^224+4752x^225+5540x^226+3960x^227+4380x^228+6140x^229+11272x^230+11060x^231+9200x^232+7640x^233+10800x^234+18740x^235+21840x^236+13700x^237+13620x^238+16100x^239+28328x^240+29280x^241+19100x^242+14100x^243+17500x^244+26620x^245+25460x^246+15060x^247+9700x^248+10160x^249+13076x^250+8020x^251+3140x^252+2180x^253+1860x^254+1952x^255+540x^256+24x^260+16x^265+16x^270

The gray image is a linear code over GF(5) with n=300, k=8 and d=220.
This code was found by Heurico 1.16 in 210 seconds.