The generator matrix

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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+680x^164+412x^165+2300x^169+628x^170+3020x^174+688x^175+4340x^179+916x^180+2160x^184+392x^185+32x^190+4x^195+28x^200+16x^205+8x^215

The gray image is a linear code over GF(5) with n=220, k=6 and d=164.
This code was found by Heurico 1.16 in 3.82 seconds.