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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 170.

Homogenous weight enumerator: w(x)=1x^0+56x^170+420x^171+1040x^172+16x^175+340x^176+320x^177+16x^180+60x^181+640x^182+16x^185+180x^186+16x^190+4x^200

The gray image is a linear code over GF(5) with n=220, k=5 and d=170.
This code was found by Heurico 1.16 in 0.161 seconds.