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

generates a code of length 73 over Z5[X]/(X^2) who´s minimum homogenous weight is 271.

Homogenous weight enumerator: w(x)=1x^0+560x^271+1080x^272+1680x^273+1800x^274+1832x^275+3120x^276+4180x^277+6500x^278+6060x^279+4736x^280+8140x^281+9400x^282+12420x^283+9440x^284+7272x^285+13060x^286+14960x^287+18640x^288+15120x^289+11504x^290+21740x^291+21160x^292+23580x^293+17900x^294+12244x^295+21860x^296+20380x^297+21440x^298+14880x^299+9304x^300+13480x^301+11280x^302+10960x^303+6400x^304+3372x^305+3040x^306+2560x^307+2280x^308+900x^309+320x^310+8x^315+8x^320+4x^325+8x^330+4x^335+4x^340+4x^345

The gray image is a linear code over GF(5) with n=365, k=8 and d=271.
This code was found by Heurico 1.16 in 468 seconds.