The generator matrix

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

generates a code of length 72 over Z5[X]/(X^2) who´s minimum homogenous weight is 267.

Homogenous weight enumerator: w(x)=1x^0+240x^267+1260x^268+2100x^269+1880x^270+1620x^271+2400x^272+5060x^273+6320x^274+6312x^275+4060x^276+4980x^277+11000x^278+13680x^279+10288x^280+7360x^281+10320x^282+16920x^283+21440x^284+15048x^285+10160x^286+14980x^287+23480x^288+27900x^289+19136x^290+12440x^291+15700x^292+23180x^293+24960x^294+15212x^295+8900x^296+9400x^297+13840x^298+11600x^299+6688x^300+2740x^301+1980x^302+2760x^303+2000x^304+1020x^305+220x^306+8x^310+20x^315+4x^320+4x^330+4x^355

The gray image is a linear code over GF(5) with n=360, k=8 and d=267.
This code was found by Heurico 1.16 in 285 seconds.