The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+524x^70+360x^71+100x^72+988x^75+1420x^76+800x^77+2264x^80+5080x^81+1600x^82+1724x^85+640x^86+64x^90+40x^95+20x^100

The gray image is a linear code over GF(5) with n=100, k=6 and d=70.
This code was found by Heurico 1.16 in 85.3 seconds.