The generator matrix

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

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+960x^57+1440x^58+48x^60+2880x^62+1920x^63+1500x^64+64x^65+4160x^67+2640x^68+12x^80

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 0.0649 seconds.