The generator matrix

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

generates a code of length 73 over Z5[X]/(X^2) who´s minimum homogenous weight is 270.

Homogenous weight enumerator: w(x)=1x^0+284x^270+40x^272+380x^274+1512x^275+400x^277+1820x^279+3244x^280+1200x^282+3240x^284+6392x^285+2300x^287+4940x^289+8592x^290+3800x^292+7840x^294+10688x^295+3460x^297+5160x^299+7196x^300+1300x^302+1620x^304+2140x^305+176x^310+132x^315+68x^320+96x^325+36x^330+52x^335+16x^340

The gray image is a linear code over GF(5) with n=365, k=7 and d=270.
This code was found by Heurico 1.16 in 13.2 seconds.