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

generates a code of length 31 over Z5[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+60x^120+500x^124+24x^125+36x^130+4x^155

The gray image is a linear code over GF(5) with n=155, k=4 and d=120.
This code was found by Heurico 1.16 in 0.00326 seconds.