The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+600x^58+160x^60+800x^63+436x^65+1100x^68+12x^70+12x^75+4x^80

The gray image is a linear code over GF(5) with n=80, k=5 and d=58.
This code was found by Heurico 1.16 in 3.2 seconds.