The generator matrix

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

generates a code of length 34 over Z5[X]/(X^2) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+60x^114+136x^115+180x^116+160x^117+100x^118+740x^119+1700x^120+860x^121+1460x^122+3080x^123+4480x^124+6168x^125+3280x^126+5140x^127+9600x^128+12940x^129+12440x^130+9400x^131+15460x^132+25020x^133+26000x^134+25408x^135+23820x^136+29080x^137+37840x^138+35200x^139+27700x^140+15660x^141+15140x^142+16860x^143+13080x^144+9480x^145+1800x^146+1060x^147+24x^150+28x^155+20x^160+12x^165+8x^170

The gray image is a linear code over GF(5) with n=170, k=8 and d=114.
This code was found by Heurico 1.16 in 99.7 seconds.