The generator matrix

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

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+240x^266+880x^267+72x^270+520x^271+560x^272+32x^275+120x^276+240x^277+4x^280+40x^281+320x^282+80x^286+16x^290

The gray image is a linear code over GF(5) with n=340, k=5 and d=266.
This code was found by Heurico 1.16 in 21.4 seconds.