The generator matrix

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

generates a code of length 70 over Z5[X]/(X^2) who´s minimum homogenous weight is 266.

Homogenous weight enumerator: w(x)=1x^0+240x^266+580x^267+168x^270+820x^271+1960x^272+160x^275+1200x^276+2180x^277+148x^280+980x^281+2300x^282+28x^285+1060x^286+2120x^287+32x^290+600x^291+860x^292+28x^295+100x^296+20x^300+4x^305+12x^310+8x^315+4x^320+4x^325+8x^330

The gray image is a linear code over GF(5) with n=350, k=6 and d=266.
This code was found by Heurico 1.16 in 90.4 seconds.