The generator matrix

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

generates a code of length 64 over Z5[X]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+1140x^236+1680x^237+920x^238+980x^239+2800x^240+4640x^241+5400x^242+3860x^243+3440x^244+6020x^245+13140x^246+12700x^247+8880x^248+5760x^249+11280x^250+20460x^251+20280x^252+14780x^253+9420x^254+17456x^255+30080x^256+27040x^257+18580x^258+10680x^259+18092x^260+28460x^261+24120x^262+14160x^263+8260x^264+10260x^265+14480x^266+9860x^267+3820x^268+1460x^269+2160x^270+2600x^271+1420x^272+24x^275+8x^280+12x^285+4x^290+4x^295+4x^300

The gray image is a linear code over GF(5) with n=320, k=8 and d=236.
This code was found by Heurico 1.16 in 247 seconds.