The generator matrix

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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 158.

Homogenous weight enumerator: w(x)=1x^0+1020x^158+620x^159+1324x^160+1600x^161+2320x^162+6460x^163+3840x^164+5340x^165+4700x^166+7100x^167+15580x^168+10920x^169+11992x^170+9160x^171+13580x^172+30600x^173+20600x^174+24956x^175+15720x^176+20260x^177+40520x^178+27580x^179+26912x^180+14280x^181+16240x^182+26420x^183+11440x^184+7512x^185+4540x^186+3000x^187+4400x^188+40x^190+8x^195+28x^200+8x^205+4x^210

The gray image is a linear code over GF(5) with n=220, k=8 and d=158.
This code was found by Heurico 1.16 in 159 seconds.