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

generates a code of length 47 over Z5[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+380x^160+800x^165+20x^168+1224x^170+400x^173+1476x^175+3200x^178+1680x^180+12800x^183+1780x^185+25600x^188+1984x^190+20480x^193+2052x^195+1860x^200+1300x^205+720x^210+256x^215+84x^220+28x^225

The gray image is a linear code over GF(5) with n=235, k=7 and d=160.
This code was found by Heurico 1.16 in 17.7 seconds.