The generator matrix

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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+1940x^74+1504x^75+580x^76+2720x^77+2020x^78+9340x^79+6628x^80+6060x^81+13440x^82+4940x^83+27840x^84+23224x^85+25140x^86+36960x^87+11560x^88+61540x^89+40644x^90+33220x^91+36880x^92+8980x^93+26840x^94+8524x^95+64x^100+36x^105

The gray image is a linear code over GF(5) with n=110, k=8 and d=74.
This code was found by Heurico 1.16 in 240 seconds.