The generator matrix

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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+100x^260+80x^262+160x^264+432x^265+220x^266+200x^267+280x^268+560x^269+1928x^270+720x^271+1140x^272+860x^273+1700x^274+3252x^275+1880x^276+1700x^277+2060x^278+1900x^279+5368x^280+2580x^281+3100x^282+3860x^283+3200x^284+7396x^285+3480x^286+3420x^287+3760x^288+2740x^289+6784x^290+2860x^291+2100x^292+1680x^293+1840x^294+2192x^295+760x^296+760x^297+400x^299+204x^300+164x^305+144x^310+44x^315+56x^320+48x^325+8x^330+4x^345

The gray image is a linear code over GF(5) with n=355, k=7 and d=260.
This code was found by Heurico 1.16 in 12.7 seconds.