The generator matrix

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

generates a code of length 73 over Z5[X]/(X^2) who´s minimum homogenous weight is 282.

Homogenous weight enumerator: w(x)=1x^0+200x^282+244x^285+400x^287+276x^290+1100x^292+800x^297+24x^300+36x^310+12x^315+20x^335+12x^340

The gray image is a linear code over GF(5) with n=365, k=5 and d=282.
This code was found by Heurico 1.16 in 25.2 seconds.