The generator matrix

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

generates a code of length 39 over Z5[X]/(X^2) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+320x^141+120x^142+560x^143+580x^144+1800x^145+1920x^146+1420x^147+2380x^148+1720x^149+3292x^150+3940x^151+2520x^152+4200x^153+2560x^154+4972x^155+6460x^156+5220x^157+6720x^158+3400x^159+5784x^160+5980x^161+3220x^162+3640x^163+1740x^164+2184x^165+1380x^166+32x^170+24x^175+20x^180+8x^185+8x^190

The gray image is a linear code over GF(5) with n=195, k=7 and d=141.
This code was found by Heurico 1.16 in 90 seconds.