The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+60x^72+300x^73+1440x^74+2040x^75+100x^76+480x^77+900x^78+1920x^79+1048x^80+400x^81+960x^82+1300x^83+2640x^84+2020x^85+12x^90+4x^95

The gray image is a linear code over GF(5) with n=100, k=6 and d=72.
This code was found by Heurico 1.16 in 96.5 seconds.