The generator matrix

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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+360x^79+88x^80+420x^81+800x^82+1320x^83+1100x^84+508x^85+1260x^86+1200x^87+860x^88+920x^89+988x^90+1820x^91+1500x^92+1320x^93+1120x^94+28x^95+12x^100

The gray image is a linear code over GF(5) with n=110, k=6 and d=79.
This code was found by Heurico 1.16 in 0.107 seconds.