The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+96x^45+244x^50+396x^55+2980x^60+10720x^65+704x^70+380x^75+104x^80

The gray image is a linear code over GF(5) with n=80, k=6 and d=45.
This code was found by Heurico 1.16 in 0.147 seconds.