The generator matrix

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

generates a code of length 12 over Z5[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+240x^45+384x^50

The gray image is a linear code over GF(5) with n=60, k=4 and d=45.
This code was found by Heurico 1.16 in 0.000295 seconds.