The generator matrix

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

generates a code of length 35 over Z5[X]/(X^2) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+720x^129+332x^130+2180x^134+672x^135+4140x^139+1112x^140+4800x^144+848x^145+660x^149+48x^150+56x^155+36x^160+16x^165+4x^175

The gray image is a linear code over GF(5) with n=175, k=6 and d=129.
This code was found by Heurico 1.16 in 24.2 seconds.