The generator matrix

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

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+160x^138+880x^139+1260x^140+1280x^141+360x^142+900x^143+3780x^144+4440x^145+2460x^146+920x^147+2340x^148+6480x^149+5504x^150+2940x^151+2080x^152+3980x^153+10680x^154+7848x^155+4120x^156+1640x^157+2620x^158+5680x^159+3976x^160+1700x^161+24x^165+24x^170+24x^175+16x^180+8x^185

The gray image is a linear code over GF(5) with n=190, k=7 and d=138.
This code was found by Heurico 1.16 in 6.49 seconds.