The generator matrix

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

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+192x^150+80x^151+200x^152+120x^155+20x^156+8x^165+4x^170

The gray image is a linear code over GF(5) with n=190, k=4 and d=150.
This code was found by Heurico 1.16 in 1.12 seconds.