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

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+72x^140+192x^145+500x^148+140x^150+2000x^153+80x^155+36x^160+40x^165+20x^170+16x^175+12x^180+16x^185

The gray image is a linear code over GF(5) with n=190, k=5 and d=140.
This code was found by Heurico 1.16 in 0.0291 seconds.