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

generates a code of length 73 over Z5[X]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+428x^260+748x^265+1112x^270+20x^272+1292x^275+400x^277+1368x^280+3200x^282+1528x^285+12800x^287+1552x^290+25600x^292+1476x^295+20480x^297+1580x^300+1380x^305+1264x^310+800x^315+612x^320+272x^325+132x^330+60x^335+20x^340

The gray image is a linear code over GF(5) with n=365, k=7 and d=260.
This code was found by Heurico 1.16 in 40.2 seconds.