The generator matrix

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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+360x^82+600x^83+60x^85+480x^87+300x^88+48x^90+660x^92+600x^93+12x^95+4x^110

The gray image is a linear code over GF(5) with n=110, k=5 and d=82.
This code was found by Heurico 1.16 in 0.0524 seconds.