The generator matrix

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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+272x^80+1024x^85+1720x^90+4x^100+88x^105+16x^110

The gray image is a linear code over GF(5) with n=110, k=5 and d=80.
This code was found by Heurico 1.16 in 35 seconds.