The generator matrix

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

generates a code of length 10 over Z5[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+720x^28+1680x^29+84x^30+3600x^32+8640x^33+7560x^34+144x^35+23000x^36+28800x^37+34560x^38+21840x^39+42644x^40+92000x^41+57600x^42+46080x^43+21420x^44+184x^45+68x^50

The gray image is a linear code over GF(5) with n=50, k=8 and d=28.
This code was found by Heurico 1.16 in 15 seconds.