The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+124x^40+564x^45+852x^50+1732x^55+15420x^60+53716x^65+3296x^70+1852x^75+568x^80

The gray image is a linear code over GF(5) with n=80, k=7 and d=40.
This code was found by Heurico 1.16 in 2.8 seconds.