The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  X  X  1  1  1  1
 0  X  0  0  0  0  0  X  X 4X 2X 3X 4X 3X 3X 3X 2X 2X  0  0 2X 2X 3X 3X 2X 2X 2X  0  0 2X 3X 4X 3X  0 3X 2X 3X 4X 4X 2X  X 4X  0 4X 4X 4X  0 4X 2X  X 4X 3X 4X  X  X  0 2X 3X  0  0  X 4X  X  X  X  X  X  X
 0  0  X  0  0  X  X 3X 4X 3X  0  X 2X 2X 4X  0 4X  X  X  0  X 3X  X 3X 4X  0 2X 2X 2X  X 4X 4X  X 3X 3X 4X 2X 4X  X  0  X  0  0  0  X  0 2X  0 2X  X  0 2X 2X  X 3X 4X 2X 2X 3X  0 4X 2X 4X 2X 2X 2X 3X 3X
 0  0  0  X  0 3X 2X 3X  X  X 4X  X  0  X 2X  X  X 2X 3X 2X  X  0  X 4X 3X 2X 4X 2X 3X 2X 2X 4X  0 3X 2X  0 2X 3X  X  X  0 4X 4X  0 3X 4X  X  X  X 3X 3X 4X 4X  X 4X  X 3X 3X 3X  X  0 2X 3X 4X 2X 4X  X 4X
 0  0  0  0  X 3X  X 4X 3X  X 3X 4X 2X  0  0  X  0 3X 2X  X  X 4X  X 2X  0 4X  0 4X  X 4X  X 2X 4X 2X 3X 2X 4X 3X 3X 4X 4X 4X 4X  X  X  0 4X  X  0 2X  0 4X  0 2X 4X  0  X 2X 4X 2X  0  0 2X 2X  X 2X  X  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+188x^250+432x^255+564x^260+1580x^265+5116x^270+6692x^275+248x^280+224x^285+220x^290+120x^295+80x^300+80x^305+52x^310+20x^315+4x^320+4x^325

The gray image is a linear code over GF(5) with n=340, k=6 and d=250.
This code was found by Heurico 1.16 in 1.15 seconds.