The generator matrix

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

generates a code of length 17 over Z5[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+16x^60+44x^65+500x^68+44x^70+8x^75+4x^80+8x^85

The gray image is a linear code over GF(5) with n=85, k=4 and d=60.
This code was found by Heurico 1.16 in 0.000841 seconds.