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

generates a code of length 37 over Z5[X]/(X^2) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+120x^142+72x^145+160x^147+24x^150+220x^152+8x^155+16x^160+4x^165

The gray image is a linear code over GF(5) with n=185, k=4 and d=142.
This code was found by Heurico 1.16 in 0.00682 seconds.