The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+140x^52+560x^53+1200x^54+148x^55+700x^56+1680x^57+2520x^58+2400x^59+1664x^60+5600x^61+6720x^62+7280x^63+9100x^64+6104x^65+11200x^66+8960x^67+7140x^68+4800x^69+104x^70+68x^75+36x^80

The gray image is a linear code over GF(5) with n=80, k=7 and d=52.
This code was found by Heurico 1.16 in 1.82 seconds.