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

generates a code of length 31 over Z5[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+148x^105+432x^110+420x^115+2920x^120+10460x^125+488x^130+368x^135+260x^140+100x^145+24x^150+4x^155

The gray image is a linear code over GF(5) with n=155, k=6 and d=105.
This code was found by Heurico 1.16 in 0.433 seconds.