The generator matrix

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

generates a code of length 35 over Z5[X]/(X^2) who´s minimum homogenous weight is 125.

Homogenous weight enumerator: w(x)=1x^0+116x^125+200x^126+500x^127+520x^128+800x^129+1504x^130+3060x^131+2460x^132+1000x^133+2000x^134+2976x^135+6120x^136+4320x^137+2280x^138+2600x^139+5552x^140+10780x^141+6480x^142+2360x^143+3600x^144+4756x^145+7340x^146+3740x^147+1340x^148+1000x^149+632x^150+40x^155+28x^160+12x^165+8x^170

The gray image is a linear code over GF(5) with n=175, k=7 and d=125.
This code was found by Heurico 1.16 in 4.72 seconds.