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

generates a code of length 35 over Z5[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+112x^120+388x^125+452x^130+500x^132+504x^135+4000x^137+400x^140+8000x^142+320x^145+436x^150+288x^155+136x^160+80x^165+8x^170

The gray image is a linear code over GF(5) with n=175, k=6 and d=120.
This code was found by Heurico 1.16 in 0.503 seconds.