The generator matrix

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

generates a code of length 34 over Z5[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+312x^110+780x^115+1196x^120+1468x^125+2032x^130+12500x^132+2332x^135+50000x^137+2632x^140+2304x^145+1496x^150+768x^155+236x^160+68x^165

The gray image is a linear code over GF(5) with n=170, k=7 and d=110.
This code was found by Heurico 1.16 in 11.2 seconds.