The generator matrix

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

generates a code of length 73 over Z5[X]/(X^2) who´s minimum homogenous weight is 286.

Homogenous weight enumerator: w(x)=1x^0+240x^286+840x^287+68x^290+520x^291+640x^292+40x^295+120x^296+240x^297+4x^300+40x^301+240x^302+80x^306+40x^307+12x^315

The gray image is a linear code over GF(5) with n=365, k=5 and d=286.
This code was found by Heurico 1.16 in 11.1 seconds.