The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1 4X  1  1  1 4X 2X  1  0 4X  1  1  1  1  1  1  1  1  1  1  1  1  1  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  3  1  2  0  3  1 3X+4 3X+1  2 X+3 X+2 3X+4  1  X X+2 2X+3 3X+1 X+2 4X+3 X+1 4X+4 3X 2X+4  0  1 4X+1 4X+3 4X+1  1  1 4X  1  1 4X+1 2X 4X+1 X+3 X+3 3X+2  1  4 X+3 3X+3 4X+1 3X+1 2X+3  3 X+2 X+3 X+3  X 4X  0 X+2 X+2 2X+2  0
 0  0 3X  0  0  0  0  X 2X 3X 2X 3X 2X 4X  0 2X  X 3X 2X  X  X 3X 2X  0 2X  X 4X 2X  0 3X 4X  X 3X  0 3X  X 2X  X 3X 2X  X 2X 2X 4X 2X 2X  X  X 4X 3X 3X 3X  X 2X 2X 3X  X 3X 2X  X 2X  0  X 3X 3X 4X  X  X 2X 3X  X 2X
 0  0  0  X  0  X 3X 3X  0 2X 2X 4X 2X 2X 3X  X  0 2X 3X  X 3X  0  0 3X 2X  X 2X 4X  X  X 4X  X  X 2X 3X  0 2X 2X 4X  X 3X 3X  0 2X 2X 3X 4X  0  0  0 4X 2X 3X 4X  0  X  X  0 2X  X 3X  X  0  X 3X  0 3X  0  0 4X 2X 3X
 0  0  0  0 3X 3X 2X 4X 4X  X 4X 4X 2X  0  0 2X 3X 3X  0  X  0  X 3X 4X 3X 3X 2X  X  X  X 4X 2X 3X 2X  X 3X  0 3X 3X 3X 4X 4X  X 2X 3X 2X 3X 2X  0 4X  0 3X  0 4X  0  0 3X 3X 3X  X  X 4X 4X 4X  0  X  X 2X  X  X 4X 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+156x^265+20x^266+20x^268+260x^269+616x^270+600x^271+380x^273+900x^274+1296x^275+3480x^276+1380x^278+1580x^279+2108x^280+4700x^281+2180x^283+2360x^284+2740x^285+9400x^286+3580x^288+2760x^289+4088x^290+11380x^291+3760x^293+2800x^294+3064x^295+6600x^296+1200x^298+1560x^299+920x^300+1320x^301+280x^304+184x^305+164x^310+112x^315+80x^320+48x^325+28x^330+16x^335+4x^340

The gray image is a linear code over GF(5) with n=360, k=7 and d=265.
This code was found by Heurico 1.16 in 13.1 seconds.