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

generates a code of length 52 over Z5[X]/(X^2) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+128x^175+508x^180+840x^185+1188x^190+100x^192+1320x^195+1600x^197+1560x^200+9600x^202+1888x^205+25600x^207+1920x^210+25600x^212+1816x^215+1776x^220+1284x^225+804x^230+400x^235+136x^240+44x^245+12x^250

The gray image is a linear code over GF(5) with n=260, k=7 and d=175.
This code was found by Heurico 1.16 in 19.6 seconds.