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

generates a code of length 55 over Z5[X]/(X^2) who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+312x^190+60x^194+748x^195+120x^199+1188x^200+1020x^204+1336x^205+3900x^209+1496x^210+11700x^214+1660x^215+18240x^219+1728x^220+19080x^224+1932x^225+8380x^229+1868x^230+1452x^235+948x^240+584x^245+284x^250+76x^255+12x^260

The gray image is a linear code over GF(5) with n=275, k=7 and d=190.
This code was found by Heurico 1.16 in 21.5 seconds.