The generator matrix

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

generates a code of length 39 over Z5[X]/(X^2) who�s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+480x^150+180x^151+520x^152+516x^155+140x^156+160x^157+448x^160+180x^161+320x^162+168x^165+4x^170+4x^175+4x^185

The gray image is a linear code over GF(5) with n=195, k=5 and d=150.
This code was found by Heurico 1.16 in 0.0159 seconds.