The generator matrix

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

generates a code of length 34 over Z5[X]/(X^2) who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+180x^122+700x^123+720x^124+392x^125+900x^126+2800x^127+3520x^128+2120x^129+692x^130+2300x^131+5520x^132+6240x^133+3320x^134+588x^135+5200x^136+9840x^137+9160x^138+4120x^139+968x^140+4100x^141+6660x^142+5380x^143+2220x^144+388x^145+40x^150+16x^155+40x^160

The gray image is a linear code over GF(5) with n=170, k=7 and d=122.
This code was found by Heurico 1.16 in 4.87 seconds.