The generator matrix

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

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+264x^220+460x^225+100x^228+424x^230+1200x^233+504x^235+4800x^238+332x^240+6400x^243+252x^245+204x^250+180x^255+152x^260+188x^265+84x^270+60x^275+16x^280+4x^285

The gray image is a linear code over GF(5) with n=300, k=6 and d=220.
This code was found by Heurico 1.16 in 39.2 seconds.