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

generates a code of length 51 over Z5[X]/(X^2) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+348x^175+804x^180+1176x^185+100x^188+1280x^190+1600x^193+1716x^195+9600x^198+1744x^200+25600x^203+1848x^205+25600x^208+2060x^210+1680x^215+1456x^220+852x^225+468x^230+144x^235+40x^240+8x^245

The gray image is a linear code over GF(5) with n=255, k=7 and d=175.
This code was found by Heurico 1.16 in 19.5 seconds.