The generator matrix

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

generates a code of length 64 over Z5[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+436x^240+880x^241+560x^242+720x^243+800x^244+2220x^245+3840x^246+1920x^247+1720x^248+1440x^249+4184x^250+5460x^251+2740x^252+2160x^253+1740x^254+4568x^255+6500x^256+3080x^257+2400x^258+1540x^259+5304x^260+6640x^261+2720x^262+2240x^263+1440x^264+3088x^265+3400x^266+1400x^267+760x^268+540x^269+744x^270+780x^271+80x^272+40x^275+16x^280+20x^285+4x^300

The gray image is a linear code over GF(5) with n=320, k=7 and d=240.
This code was found by Heurico 1.16 in 9.49 seconds.