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

generates a code of length 31 over Z5[X]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+232x^115+100x^116+116x^120+800x^121+76x^125+1600x^126+80x^130+88x^140+24x^145+8x^150

The gray image is a linear code over GF(5) with n=155, k=5 and d=115.
This code was found by Heurico 1.16 in 2.27 seconds.