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

generates a code of length 64 over Z5[X]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+404x^225+720x^230+1120x^235+80x^237+1304x^240+1000x^242+1528x^245+5200x^247+1420x^250+15100x^252+1756x^255+24800x^257+1732x^260+16320x^262+1668x^265+1472x^270+1048x^275+740x^280+408x^285+208x^290+80x^295+12x^300+4x^305

The gray image is a linear code over GF(5) with n=320, k=7 and d=225.
This code was found by Heurico 1.16 in 41.4 seconds.