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

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+460x^139+2216x^140+480x^141+2240x^143+2020x^144+6804x^145+1120x^146+4320x^148+3780x^149+9520x^150+960x^151+8000x^153+5540x^154+12884x^155+1800x^156+5280x^158+3200x^159+6608x^160+640x^161+20x^165+32x^170+20x^175+12x^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 6.38 seconds.