The generator matrix

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

generates a code of length 52 over Z5[X]/(X^2) who´s minimum homogenous weight is 185.

Homogenous weight enumerator: w(x)=1x^0+108x^185+40x^188+80x^189+480x^190+340x^191+380x^193+700x^194+1344x^195+2000x^196+1260x^198+1300x^199+2096x^200+5200x^201+2260x^203+2500x^204+2944x^205+11000x^206+3760x^208+4000x^209+3940x^210+12700x^211+3520x^213+2820x^214+3144x^215+6260x^216+1280x^218+1100x^219+1008x^220+224x^225+156x^230+132x^235+36x^240+8x^245+4x^250

The gray image is a linear code over GF(5) with n=260, k=7 and d=185.
This code was found by Heurico 1.16 in 9.4 seconds.