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

generates a code of length 35 over Z5[X]/(X^2) who´s minimum homogenous weight is 130.

Homogenous weight enumerator: w(x)=1x^0+144x^130+100x^132+184x^135+800x^137+112x^140+1600x^142+72x^145+28x^150+24x^155+24x^160+16x^165+16x^170+4x^175

The gray image is a linear code over GF(5) with n=175, k=5 and d=130.
This code was found by Heurico 1.16 in 0.0471 seconds.