The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  0  1  0  0  1  1  1  1  1
 0  1  1  2  4  3  0 3X+1  2 3X+4  3  1 3X+4  1  1 3X+4  3  0  0  0
 0  0 3X  0  0  X  0 3X 3X 3X 2X 4X 3X 2X 4X 2X 4X  X 3X  0
 0  0  0  X  0 3X 2X 2X  X  X  0 4X 4X 3X 3X 2X 3X  X  0  0
 0  0  0  0 3X 4X 4X  X 4X  0 2X  X 4X 4X  X 3X 3X  X  0  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+108x^60+40x^64+504x^65+100x^68+640x^69+1424x^70+1000x^72+1200x^73+3840x^74+2700x^75+8000x^77+4800x^78+10240x^79+4380x^80+16000x^82+6400x^83+10240x^84+5772x^85+496x^90+216x^95+24x^100

The gray image is a linear code over GF(5) with n=100, k=7 and d=60.
This code was found by Heurico 1.16 in 2.38 seconds.