The generator matrix

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

generates a code of length 52 over Z5[X]/(X^2) who´s minimum homogenous weight is 189.

Homogenous weight enumerator: w(x)=1x^0+660x^189+1188x^190+2000x^191+840x^192+1120x^193+4840x^194+6328x^195+6820x^196+3340x^197+3840x^198+11880x^199+12220x^200+14660x^201+7480x^202+8580x^203+22760x^204+22548x^205+23240x^206+13340x^207+14820x^208+32640x^209+29848x^210+27920x^211+14500x^212+13660x^213+27260x^214+20676x^215+16700x^216+5320x^217+2980x^218+7460x^219+5220x^220+3660x^221+180x^222+36x^225+24x^230+24x^235+8x^240+4x^245

The gray image is a linear code over GF(5) with n=260, k=8 and d=189.
This code was found by Heurico 1.16 in 177 seconds.