The generator matrix

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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+496x^175+120x^180+8x^200

The gray image is a linear code over GF(5) with n=220, k=4 and d=175.
This code was found by Heurico 1.16 in 1.84 seconds.