The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+600x^57+1800x^58+660x^60+1800x^62+2400x^63+2440x^65+2600x^67+3300x^68+24x^75

The gray image is a linear code over GF(5) with n=80, k=6 and d=57.
This code was found by Heurico 1.16 in 0.0852 seconds.