The generator matrix

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

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+968x^135+1680x^136+1780x^137+800x^138+1740x^139+6764x^140+7080x^141+6200x^142+2660x^143+4800x^144+17480x^145+18000x^146+13020x^147+7340x^148+11960x^149+40680x^150+33520x^151+23940x^152+13520x^153+17720x^154+51528x^155+35740x^156+19360x^157+7800x^158+8780x^159+18100x^160+11480x^161+5700x^162+380x^163+24x^165+32x^170+36x^175+4x^180+4x^185+4x^190

The gray image is a linear code over GF(5) with n=190, k=8 and d=135.
This code was found by Heurico 1.16 in 121 seconds.