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

generates a code of length 34 over Z5[X]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+88x^115+356x^120+412x^125+500x^128+396x^130+4000x^133+480x^135+8000x^138+388x^140+440x^145+312x^150+184x^155+60x^160+4x^165+4x^170

The gray image is a linear code over GF(5) with n=170, k=6 and d=115.
This code was found by Heurico 1.16 in 0.48 seconds.