The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+84x^60+272x^65+384x^70+460x^75+13020x^80+676x^85+488x^90+216x^95+24x^100

The gray image is a linear code over GF(5) with n=100, k=6 and d=60.
This code was found by Heurico 1.16 in 0.216 seconds.