The generator matrix

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

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+2360x^120+4824x^125+5180x^130+3240x^135+20x^150

The gray image is a linear code over GF(5) with n=160, k=6 and d=120.
This code was found by Heurico 1.16 in 58 seconds.