The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+400x^54+144x^55+200x^56+800x^59+1176x^60+1600x^61+2200x^64+4096x^65+3200x^66+1600x^69+96x^70+80x^75+32x^80

The gray image is a linear code over GF(5) with n=80, k=6 and d=54.
This code was found by Heurico 1.16 in 20.1 seconds.