The generator matrix

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

generates a code of length 35 over Z5[X]/(X^2) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+760x^123+1780x^124+832x^125+720x^126+2320x^127+4380x^128+7680x^129+4584x^130+3340x^131+7500x^132+14380x^133+18900x^134+10852x^135+10160x^136+17280x^137+31580x^138+37620x^139+21796x^140+17780x^141+28160x^142+40380x^143+39940x^144+17744x^145+10500x^146+12240x^147+13520x^148+11580x^149+2220x^150+44x^155+36x^160+12x^165+4x^170

The gray image is a linear code over GF(5) with n=175, k=8 and d=123.
This code was found by Heurico 1.16 in 109 seconds.