The generator matrix

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

generates a code of length 72 over Z5[X]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+732x^275+3560x^280+3120x^285+3600x^290+3328x^295+1128x^300+96x^305+12x^310+12x^315+8x^320+20x^325+4x^335+4x^340

The gray image is a linear code over GF(5) with n=360, k=6 and d=275.
This code was found by Heurico 1.16 in 0.562 seconds.