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

generates a code of length 69 over Z5[X]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+200x^266+400x^270+400x^271+112x^275+1100x^276+800x^281+80x^295+8x^300+20x^320+4x^325

The gray image is a linear code over GF(5) with n=345, k=5 and d=266.
This code was found by Heurico 1.16 in 62.8 seconds.