The generator matrix

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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+256x^65+768x^70+1288x^75+4368x^80+22756x^85+43364x^90+2992x^95+1636x^100+572x^105+124x^110

The gray image is a linear code over GF(5) with n=110, k=7 and d=65.
This code was found by Heurico 1.16 in 5.79 seconds.