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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+120x^70+400x^75+424x^80+476x^85+12500x^88+600x^90+600x^95+364x^100+116x^105+24x^110

The gray image is a linear code over GF(5) with n=110, k=6 and d=70.
This code was found by Heurico 1.16 in 0.266 seconds.