The generator matrix

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

generates a code of length 39 over Z5[X]/(X^2) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+740x^139+1748x^140+2860x^141+840x^142+2180x^143+4140x^144+8296x^145+7420x^146+3220x^147+6680x^148+11220x^149+19644x^150+16000x^151+7880x^152+19780x^153+25300x^154+33200x^155+26880x^156+13640x^157+33180x^158+31480x^159+36564x^160+24260x^161+9000x^162+10680x^163+12120x^164+13588x^165+7580x^166+420x^167+20x^170+16x^175+16x^180+32x^185

The gray image is a linear code over GF(5) with n=195, k=8 and d=139.
This code was found by Heurico 1.16 in 125 seconds.