The generator matrix

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

generates a code of length 21 over Z5[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+1744x^70+1080x^71+580x^72+3020x^73+3060x^74+7580x^75+4440x^76+6960x^77+14340x^78+7820x^79+25048x^80+17600x^81+27840x^82+40260x^83+22680x^84+56076x^85+31160x^86+37120x^87+39880x^88+13940x^89+22576x^90+5720x^91+52x^95+40x^100+8x^105

The gray image is a linear code over GF(5) with n=105, k=8 and d=70.
This code was found by Heurico 1.16 in 74.2 seconds.