The generator matrix

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

generates a code of length 64 over Z5[X]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+1020x^244+368x^245+2580x^249+712x^250+2580x^254+648x^255+3580x^259+960x^260+2180x^264+356x^265+560x^269+12x^270+20x^275+16x^280+4x^285+12x^290+8x^295+4x^305+4x^310

The gray image is a linear code over GF(5) with n=320, k=6 and d=244.
This code was found by Heurico 1.16 in 14.9 seconds.