The generator matrix

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

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 250.

Homogenous weight enumerator: w(x)=1x^0+316x^250+60x^253+280x^254+660x^255+220x^256+1580x^258+1960x^259+1400x^260+960x^261+2740x^263+3160x^264+2404x^265+2160x^266+4640x^268+5260x^269+2916x^270+3560x^271+7940x^273+7460x^274+3948x^275+3960x^276+5980x^278+5180x^279+2552x^280+1640x^281+2060x^283+1700x^284+900x^285+148x^290+116x^295+136x^300+68x^305+20x^310+28x^315+8x^320+4x^325

The gray image is a linear code over GF(5) with n=340, k=7 and d=250.
This code was found by Heurico 1.16 in 12.4 seconds.