The generator matrix

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

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+48x^45+20x^48+252x^50+300x^52+320x^53+408x^55+500x^56+3600x^57+1920x^58+2980x^60+4000x^61+14400x^62+5120x^63+10820x^65+8000x^66+19200x^67+5120x^68+672x^70+372x^75+72x^80

The gray image is a linear code over GF(5) with n=80, k=7 and d=45.
This code was found by Heurico 1.16 in 1.59 seconds.