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

generates a code of length 53 over Z5[X]/(X^2) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+104x^180+560x^185+1028x^190+1176x^195+2000x^200+7640x^205+25888x^210+33780x^215+1864x^220+1616x^225+1312x^230+712x^235+312x^240+100x^245+28x^250+4x^255

The gray image is a linear code over GF(5) with n=265, k=7 and d=180.
This code was found by Heurico 1.16 in 20.2 seconds.