The generator matrix

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

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 255.

Homogenous weight enumerator: w(x)=1x^0+332x^255+560x^256+160x^257+1360x^259+3164x^260+2780x^261+760x^262+3540x^264+5248x^265+4260x^266+1260x^267+4440x^269+6840x^270+5140x^271+820x^272+4640x^274+7556x^275+4720x^276+980x^277+4440x^279+5336x^280+3840x^281+780x^282+1580x^284+2080x^285+1200x^286+240x^287+20x^290+8x^295+20x^300+4x^305+8x^310+4x^315+4x^320

The gray image is a linear code over GF(5) with n=340, k=7 and d=255.
This code was found by Heurico 1.16 in 10.8 seconds.