The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1 3X  1 2X  1  1  X  1  1
 0  1  0 3X+1  2  4 3X  1 X+4 2X 4X+1 4X+2  1 3X+2  1 3X+4 2X  1 X+2  X
 0  0  1 3X+3  2  1 3X+1 X+4 3X+4 X+2  X X+1 4X+4 2X+4 4X+2 4X+3 4X+2 2X+4  2 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+188x^70+160x^71+120x^73+1000x^74+1788x^75+840x^76+360x^78+1600x^79+2016x^80+2640x^81+520x^83+1900x^84+2108x^85+360x^86+24x^95

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 0.0986 seconds.