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

generates a code of length 72 over Z5[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+148x^265+416x^270+408x^275+100x^276+388x^280+1200x^281+356x^285+4800x^286+340x^290+6400x^291+308x^295+156x^300+156x^305+136x^310+148x^315+52x^320+60x^325+16x^330+28x^335+4x^340+4x^345

The gray image is a linear code over GF(5) with n=360, k=6 and d=265.
This code was found by Heurico 1.16 in 1.22 seconds.