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

generates a code of length 44 over Z5[X]/(X^2) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+88x^145+520x^150+896x^155+100x^157+1232x^160+1000x^162+1576x^165+5000x^167+1840x^170+15500x^172+1992x^175+24500x^177+2236x^180+16400x^182+1916x^185+1684x^190+1012x^195+432x^200+168x^205+32x^210

The gray image is a linear code over GF(5) with n=220, k=7 and d=145.
This code was found by Heurico 1.16 in 16 seconds.