The generator matrix

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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 263.

Homogenous weight enumerator: w(x)=1x^0+480x^263+1020x^264+1732x^265+1660x^266+1420x^267+2960x^268+4980x^269+7448x^270+4800x^271+2840x^272+6500x^273+10640x^274+14368x^275+9060x^276+5920x^277+12540x^278+18120x^279+22344x^280+12440x^281+8480x^282+18640x^283+24500x^284+29388x^285+15540x^286+9220x^287+19360x^288+25260x^289+25668x^290+12280x^291+7340x^292+11580x^293+13280x^294+12548x^295+5840x^296+2160x^297+2940x^298+2200x^299+2068x^300+880x^301+120x^302+32x^305+12x^310+4x^320+8x^325+4x^330

The gray image is a linear code over GF(5) with n=355, k=8 and d=263.
This code was found by Heurico 1.16 in 280 seconds.