The generator matrix

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

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+148x^70+80x^73+280x^74+344x^75+300x^76+680x^78+880x^79+912x^80+3600x^81+2480x^83+3180x^84+4540x^85+14400x^86+5180x^88+4880x^89+8600x^90+19200x^91+4080x^93+3280x^94+592x^95+320x^100+148x^105+20x^110

The gray image is a linear code over GF(5) with n=110, k=7 and d=70.
This code was found by Heurico 1.16 in 2.84 seconds.