The generator matrix

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

generates a code of length 60 over Z5[X]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+1148x^225+980x^226+1040x^227+180x^228+400x^229+3944x^230+4120x^231+2540x^232+680x^233+500x^234+5740x^235+6220x^236+3360x^237+480x^238+440x^239+7648x^240+6920x^241+3780x^242+480x^243+680x^244+7840x^245+6620x^246+3000x^247+480x^248+320x^249+3788x^250+2640x^251+1280x^252+200x^253+160x^254+452x^255+20x^260+12x^265+20x^270+8x^275+4x^280

The gray image is a linear code over GF(5) with n=300, k=7 and d=225.
This code was found by Heurico 1.16 in 82.7 seconds.