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

generates a code of length 64 over Z5[X]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+152x^245+168x^250+500x^252+88x^255+2000x^257+88x^260+36x^265+24x^270+16x^275+12x^280+12x^285+20x^290+4x^295+4x^315

The gray image is a linear code over GF(5) with n=320, k=5 and d=245.
This code was found by Heurico 1.16 in 0.0747 seconds.