The generator matrix

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

generates a code of length 34 over Z5[X]/(X^2) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+660x^127+1040x^128+360x^129+12x^130+2820x^132+1980x^133+480x^134+48x^135+1980x^137+1320x^138+360x^139+64x^140+2540x^142+1660x^143+300x^144

The gray image is a linear code over GF(5) with n=170, k=6 and d=127.
This code was found by Heurico 1.16 in 0.177 seconds.