The generator matrix

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

generates a code of length 40 over Z5[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+724x^150+500x^151+400x^152+120x^153+160x^154+1644x^155+1760x^156+1160x^157+160x^158+160x^159+1604x^160+1580x^161+680x^162+120x^163+100x^164+1184x^165+1660x^166+760x^167+100x^168+80x^169+964x^170+4x^175

The gray image is a linear code over GF(5) with n=200, k=6 and d=150.
This code was found by Heurico 1.16 in 0.22 seconds.