The generator matrix

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

generates a code of length 70 over Z5[X]/(X^2) who´s minimum homogenous weight is 270.

Homogenous weight enumerator: w(x)=1x^0+840x^270+1280x^271+680x^272+180x^273+180x^274+2008x^275+1360x^276+920x^277+80x^278+160x^279+1284x^280+1100x^281+620x^282+140x^283+80x^284+824x^285+880x^286+480x^287+60x^288+40x^289+600x^290+700x^291+300x^292+40x^293+40x^294+564x^295+180x^296+4x^315

The gray image is a linear code over GF(5) with n=350, k=6 and d=270.
This code was found by Heurico 1.16 in 3.15 seconds.