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

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+76x^265+260x^266+200x^267+560x^268+364x^270+480x^271+200x^272+240x^273+60x^275+100x^276+40x^278+64x^280+120x^281+100x^282+160x^283+52x^285+40x^286+4x^290+4x^295

The gray image is a linear code over GF(5) with n=340, k=5 and d=265.
This code was found by Heurico 1.16 in 0.0582 seconds.