The generator matrix

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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 270.

Homogenous weight enumerator: w(x)=1x^0+240x^270+220x^272+400x^273+2156x^275+580x^277+520x^278+1972x^280+580x^282+520x^283+2616x^285+380x^287+420x^288+2624x^290+580x^292+520x^293+920x^295+160x^297+120x^298+40x^300+20x^305+8x^315+16x^320+4x^325+4x^330+4x^340

The gray image is a linear code over GF(5) with n=355, k=6 and d=270.
This code was found by Heurico 1.16 in 0.55 seconds.