The generator matrix

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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+144x^155+100x^156+40x^158+80x^159+384x^160+260x^161+520x^162+1020x^163+840x^164+452x^165+1240x^166+1920x^167+2420x^168+1440x^169+404x^170+2340x^171+6120x^172+7220x^173+3840x^174+388x^175+3940x^176+9920x^177+9020x^178+4240x^179+304x^180+3240x^181+6520x^182+5280x^183+2060x^184+392x^185+1380x^186+288x^190+156x^195+156x^200+52x^205+4x^210

The gray image is a linear code over GF(5) with n=220, k=7 and d=155.
This code was found by Heurico 1.16 in 7.45 seconds.