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

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+76x^260+100x^264+200x^265+800x^269+132x^270+1600x^274+92x^275+28x^280+36x^285+12x^290+8x^295+12x^300+8x^305+8x^310+8x^315+4x^330

The gray image is a linear code over GF(5) with n=340, k=5 and d=260.
This code was found by Heurico 1.16 in 0.0848 seconds.