The generator matrix

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

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+204x^270+440x^275+20x^276+444x^280+320x^281+412x^285+1920x^286+308x^290+5120x^291+292x^295+5120x^296+232x^300+212x^305+184x^310+100x^315+120x^320+88x^325+44x^330+24x^335+12x^340+4x^345+4x^350

The gray image is a linear code over GF(5) with n=365, k=6 and d=270.
This code was found by Heurico 1.16 in 1.24 seconds.