The generator matrix

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

generates a code of length 73 over Z5[X]/(X^2) who´s minimum homogenous weight is 282.

Homogenous weight enumerator: w(x)=1x^0+1340x^282+1320x^283+300x^284+32x^285+2060x^287+1700x^288+540x^289+56x^290+1880x^292+1080x^293+300x^294+1240x^297+920x^298+180x^299+940x^302+720x^303+180x^304+12x^305+540x^307+260x^308+16x^310+8x^315

The gray image is a linear code over GF(5) with n=365, k=6 and d=282.
This code was found by Heurico 1.16 in 18.6 seconds.