The generator matrix

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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+512x^75+160x^76+420x^77+780x^78+700x^79+2896x^80+1920x^81+2340x^82+1660x^83+900x^84+7272x^85+7680x^86+6060x^87+4340x^88+2100x^89+14212x^90+10240x^91+6180x^92+3220x^93+1300x^94+3132x^95+64x^100+36x^105

The gray image is a linear code over GF(5) with n=110, k=7 and d=75.
This code was found by Heurico 1.16 in 2.54 seconds.