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

generates a code of length 72 over Z5[X]/(X^2) who´s minimum homogenous weight is 282.

Homogenous weight enumerator: w(x)=1x^0+360x^282+640x^283+48x^285+800x^287+480x^288+60x^290+120x^292+120x^293+120x^297+260x^298+4x^300+100x^302+12x^310

The gray image is a linear code over GF(5) with n=360, k=5 and d=282.
This code was found by Heurico 1.16 in 1.25 seconds.