The generator matrix

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

generates a code of length 72 over Z5[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+960x^272+940x^273+920x^274+740x^275+3200x^277+3220x^278+2380x^279+1992x^280+6000x^282+4480x^283+3260x^284+2284x^285+6880x^287+5060x^288+3360x^289+2596x^290+6360x^292+4840x^293+2760x^294+1964x^295+4880x^297+2980x^298+1940x^299+964x^300+1720x^302+980x^303+380x^304+28x^305+16x^310+8x^315+20x^320+4x^325+4x^330+4x^335

The gray image is a linear code over GF(5) with n=360, k=7 and d=272.
This code was found by Heurico 1.16 in 38.8 seconds.