The generator matrix

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

generates a code of length 17 over Z5[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+84x^65+180x^66+80x^67+132x^70+120x^71+20x^72+8x^75

The gray image is a linear code over GF(5) with n=85, k=4 and d=65.
This code was found by Heurico 1.16 in 0.000568 seconds.