The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+784x^50+1280x^52+1760x^53+2720x^54+3580x^55+2400x^56+12360x^57+9120x^58+6840x^59+18716x^60+19200x^61+52440x^62+24480x^63+25660x^64+54536x^65+38400x^66+68920x^67+24640x^68+12280x^69+10416x^70+76x^75+16x^80

The gray image is a linear code over GF(5) with n=80, k=8 and d=50.
This code was found by Heurico 1.16 in 37.9 seconds.