The generator matrix

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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+500x^161+700x^162+240x^163+1200x^164+1144x^165+1960x^166+2040x^167+940x^168+3200x^169+2128x^170+4040x^171+4720x^172+2040x^173+5600x^174+2624x^175+6120x^176+6600x^177+2640x^178+6400x^179+3100x^180+5300x^181+4980x^182+1640x^183+3600x^184+1540x^185+2080x^186+960x^187+36x^190+20x^195+8x^200+8x^205+8x^210+8x^215

The gray image is a linear code over GF(5) with n=220, k=7 and d=161.
This code was found by Heurico 1.16 in 14.5 seconds.