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

generates a code of length 32 over Z5[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+260x^120+500x^124+104x^125+2000x^129+160x^130+40x^145+20x^150+40x^155

The gray image is a linear code over GF(5) with n=160, k=5 and d=120.
This code was found by Heurico 1.16 in 2.82 seconds.