The generator matrix

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

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+980x^260+400x^262+360x^263+2652x^265+560x^267+420x^268+1964x^270+420x^272+1080x^273+2140x^275+880x^277+640x^278+2084x^280+240x^282+740x^285+28x^290+8x^300+16x^305+4x^310+4x^315+4x^330

The gray image is a linear code over GF(5) with n=340, k=6 and d=260.
This code was found by Heurico 1.16 in 2.68 seconds.