The generator matrix

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

generates a code of length 73 over Z5[X]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+388x^275+620x^276+660x^277+300x^278+820x^279+1748x^280+4300x^281+1700x^282+840x^283+1740x^284+3344x^285+6320x^286+2460x^287+820x^288+2060x^289+3964x^290+6980x^291+2840x^292+1360x^293+2460x^294+3968x^295+7140x^296+2320x^297+1100x^298+1960x^299+3040x^300+5280x^301+2040x^302+440x^303+840x^304+1544x^305+1860x^306+480x^307+140x^308+120x^309+84x^310+8x^315+4x^320+28x^325+4x^335

The gray image is a linear code over GF(5) with n=365, k=7 and d=275.
This code was found by Heurico 1.16 in 11.8 seconds.