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

generates a code of length 34 over Z5[X]/(X^2) who´s minimum homogenous weight is 125.

Homogenous weight enumerator: w(x)=1x^0+96x^125+212x^130+500x^132+100x^135+2000x^137+88x^140+40x^145+32x^150+12x^155+24x^160+16x^165+4x^170

The gray image is a linear code over GF(5) with n=170, k=5 and d=125.
This code was found by Heurico 1.16 in 0.0245 seconds.