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

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 130.

Homogenous weight enumerator: w(x)=1x^0+72x^130+280x^135+448x^140+456x^145+2500x^148+428x^150+10000x^153+400x^155+348x^160+312x^165+224x^170+116x^175+28x^180+12x^185

The gray image is a linear code over GF(5) with n=190, k=6 and d=130.
This code was found by Heurico 1.16 in 0.552 seconds.