The generator matrix

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

generates a code of length 45 over Z5[X]/(X^2) who´s minimum homogenous weight is 179.

Homogenous weight enumerator: w(x)=1x^0+400x^179+116x^180+100x^184+4x^200+4x^205

The gray image is a linear code over GF(5) with n=225, k=4 and d=179.
This code was found by Heurico 1.16 in 1.43 seconds.