The generator matrix

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

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+300x^143+1340x^144+1116x^145+680x^146+900x^148+1480x^149+1416x^150+600x^151+900x^153+1420x^154+1188x^155+360x^156+900x^158+1760x^159+904x^160+360x^161

The gray image is a linear code over GF(5) with n=190, k=6 and d=143.
This code was found by Heurico 1.16 in 4.97 seconds.