The generator matrix

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

generates a code of length 55 over Z5[X]/(X^2) who´s minimum homogenous weight is 201.

Homogenous weight enumerator: w(x)=1x^0+560x^201+1760x^202+2000x^203+1920x^204+1836x^205+3680x^206+6700x^207+6280x^208+5300x^209+3828x^210+8440x^211+16060x^212+12440x^213+9800x^214+9716x^215+17380x^216+26640x^217+19640x^218+14960x^219+14804x^220+26520x^221+37120x^222+24040x^223+14820x^224+13208x^225+20800x^226+25540x^227+14340x^228+9260x^229+4636x^230+5120x^231+6180x^232+3760x^233+1440x^234+20x^235+32x^240+28x^245+8x^250+4x^260+4x^265

The gray image is a linear code over GF(5) with n=275, k=8 and d=201.
This code was found by Heurico 1.16 in 516 seconds.