The generator matrix

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

generates a code of length 69 over Z5[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+484x^265+940x^266+240x^267+600x^268+360x^269+1516x^270+1440x^271+360x^272+800x^273+200x^274+1176x^275+1180x^276+520x^277+460x^278+180x^279+808x^280+940x^281+240x^282+280x^283+200x^284+680x^285+620x^286+120x^287+360x^288+60x^289+448x^290+380x^291+20x^292+8x^295+4x^300

The gray image is a linear code over GF(5) with n=345, k=6 and d=265.
This code was found by Heurico 1.16 in 0.424 seconds.