The generator matrix

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

generates a code of length 70 over Z5[X]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+1024x^260+1960x^261+1940x^262+2000x^263+2020x^264+4136x^265+7280x^266+6140x^267+4960x^268+4700x^269+8672x^270+13280x^271+11320x^272+9060x^273+7700x^274+16676x^275+21100x^276+18200x^277+13880x^278+11800x^279+22928x^280+27180x^281+22500x^282+15160x^283+11800x^284+21104x^285+25000x^286+17460x^287+11240x^288+7580x^289+11412x^290+12260x^291+6760x^292+3460x^293+1900x^294+2100x^295+1940x^296+680x^297+240x^298+44x^300+8x^305+8x^310+8x^315+4x^320

The gray image is a linear code over GF(5) with n=350, k=8 and d=260.
This code was found by Heurico 1.16 in 421 seconds.