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

generates a code of length 70 over Z5[X]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+112x^245+528x^250+884x^255+1124x^260+1344x^265+500x^268+1516x^270+6000x^273+1504x^275+24000x^278+1680x^280+32000x^283+1404x^285+1680x^290+1280x^295+1052x^300+812x^305+428x^310+196x^315+52x^320+20x^325+4x^330+4x^335

The gray image is a linear code over GF(5) with n=350, k=7 and d=245.
This code was found by Heurico 1.16 in 28.4 seconds.