The generator matrix

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

generates a code of length 35 over Z5[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+128x^120+20x^122+120x^123+20x^124+568x^125+240x^126+480x^127+660x^128+320x^129+1760x^130+1040x^131+1380x^132+1760x^133+1920x^134+5444x^135+2940x^136+3280x^137+3560x^138+5120x^139+10732x^140+5040x^141+4780x^142+4360x^143+5120x^144+8620x^145+3240x^146+2560x^147+2040x^148+316x^150+340x^155+156x^160+48x^165+12x^170

The gray image is a linear code over GF(5) with n=175, k=7 and d=120.
This code was found by Heurico 1.16 in 5.56 seconds.