The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  X  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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+80x^61+240x^62+16x^65+120x^66+160x^67+8x^70

The gray image is a linear code over GF(5) with n=80, k=4 and d=61.
This code was found by Heurico 1.16 in 0.000501 seconds.