The generator matrix

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

generates a code of length 51 over Z5[X]/(X^2) who´s minimum homogenous weight is 185.

Homogenous weight enumerator: w(x)=1x^0+608x^185+1300x^186+1140x^187+900x^188+2080x^189+4244x^190+7000x^191+4360x^192+4120x^193+5500x^194+11776x^195+14080x^196+9520x^197+7660x^198+12260x^199+21972x^200+25940x^201+15780x^202+15120x^203+18920x^204+31428x^205+34200x^206+18840x^207+15980x^208+17980x^209+26304x^210+24660x^211+10760x^212+6040x^213+5760x^214+6688x^215+5320x^216+2100x^217+180x^218+44x^220+32x^225+12x^230+8x^235+8x^240

The gray image is a linear code over GF(5) with n=255, k=8 and d=185.
This code was found by Heurico 1.16 in 172 seconds.