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

generates a code of length 72 over Z5[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+300x^280+1024x^285+1720x^290+32x^305+16x^310+28x^330+4x^350

The gray image is a linear code over GF(5) with n=360, k=5 and d=280.
This code was found by Heurico 1.16 in 22.3 seconds.