The generator matrix

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

generates a code of length 69 over Z5[X]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+536x^260+1320x^261+980x^262+200x^263+3160x^265+4240x^266+2620x^267+400x^268+5132x^270+6740x^271+3880x^272+520x^273+5596x^275+7500x^276+4040x^277+640x^278+5776x^280+7360x^281+3700x^282+560x^283+3976x^285+4200x^286+1980x^287+180x^288+1368x^290+1140x^291+300x^292+44x^295+20x^300+4x^310+8x^315+4x^325

The gray image is a linear code over GF(5) with n=345, k=7 and d=260.
This code was found by Heurico 1.16 in 10.9 seconds.