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

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+100x^185+348x^190+412x^195+452x^200+368x^205+12500x^208+288x^210+264x^215+360x^220+228x^225+112x^230+128x^235+28x^240+28x^245+4x^250+4x^260

The gray image is a linear code over GF(5) with n=260, k=6 and d=185.
This code was found by Heurico 1.16 in 0.819 seconds.