The generator matrix

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

generates a code of length 16 over Z5[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+144x^55+100x^56+176x^60+800x^61+96x^65+1600x^66+96x^70+80x^75+32x^80

The gray image is a linear code over GF(5) with n=80, k=5 and d=55.
This code was found by Heurico 1.16 in 0.00801 seconds.