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

generates a code of length 48 over Z5[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+96x^160+480x^165+840x^170+1268x^175+100x^176+1420x^180+1600x^181+1812x^185+9600x^186+1816x^190+25600x^191+2100x^195+25600x^196+1948x^200+1692x^205+1192x^210+624x^215+240x^220+88x^225+8x^230

The gray image is a linear code over GF(5) with n=240, k=7 and d=160.
This code was found by Heurico 1.16 in 17.8 seconds.