The generator matrix

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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+860x^166+120x^167+660x^168+220x^169+540x^170+2500x^171+280x^172+1040x^173+360x^174+472x^175+2120x^176+280x^177+840x^178+220x^179+348x^180+1820x^181+320x^182+960x^183+200x^184+248x^185+1200x^186+8x^190+8x^195

The gray image is a linear code over GF(5) with n=220, k=6 and d=166.
This code was found by Heurico 1.16 in 0.254 seconds.