The generator matrix

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

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+360x^141+60x^142+300x^143+720x^144+872x^145+1060x^146+300x^147+720x^148+1300x^149+1148x^150+1220x^151+220x^152+660x^153+840x^154+872x^155+1040x^156+420x^157+820x^158+1140x^159+720x^160+820x^161+8x^165+4x^170

The gray image is a linear code over GF(5) with n=190, k=6 and d=141.
This code was found by Heurico 1.16 in 0.208 seconds.