The generator matrix

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

generates a code of length 29 over Z5[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+156x^90+748x^95+1120x^100+3120x^105+11792x^110+28100x^115+28500x^120+2424x^125+1380x^130+608x^135+164x^140+12x^145

The gray image is a linear code over GF(5) with n=145, k=7 and d=90.
This code was found by Heurico 1.16 in 8.8 seconds.