The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1
 0  X  0  0  0  0  0  X  X  X 3X 4X 2X  X  X 2X 2X 2X  0  X 4X  0 2X  X 2X 2X  0  X 3X 4X 2X 2X 4X 4X  X  0 4X  0  X  X 2X  0 2X  0
 0  0  X  0  0  X  X 3X 4X 2X 3X 3X  0 2X  X  X  X 4X 4X  0 2X 3X 2X 4X  0  0 4X 3X 3X  0  0 3X 2X 2X  X 2X 4X 4X 4X  X  X 3X 2X  0
 0  0  0  X  0 3X 2X 3X  X 3X 3X 3X 4X  X 3X  0 4X 3X  X 2X  X  X 4X 4X 2X 2X  X  X 4X  X  0  0 2X  X 2X 2X  0 3X 4X 2X  0 4X  0  0
 0  0  0  0  X 3X  X 4X 3X 2X  0 2X 4X 2X 3X 4X 3X 3X 4X 4X  0 2X 4X 3X 2X 3X 3X 3X  X 2X 3X 4X 2X 4X 3X  X 4X 3X 2X  0 2X 4X 2X 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+140x^155+372x^160+464x^165+428x^170+2500x^172+360x^175+10000x^177+332x^180+372x^185+268x^190+212x^195+124x^200+28x^205+16x^210+8x^215

The gray image is a linear code over GF(5) with n=220, k=6 and d=155.
This code was found by Heurico 1.16 in 0.667 seconds.