The generator matrix

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

generates a code of length 34 over Z5[X]/(X^2) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+940x^119+1360x^120+700x^121+360x^122+2740x^123+5680x^124+5744x^125+3600x^126+2780x^127+9040x^128+16300x^129+16044x^130+11720x^131+7000x^132+21740x^133+35020x^134+32636x^135+21740x^136+15220x^137+33940x^138+45640x^139+33604x^140+18460x^141+7140x^142+15040x^143+16420x^144+8632x^145+1280x^146+52x^150+28x^155+16x^160+8x^165

The gray image is a linear code over GF(5) with n=170, k=8 and d=119.
This code was found by Heurico 1.16 in 105 seconds.