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

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+1460x^272+840x^273+620x^274+224x^275+5640x^277+1280x^278+2340x^279+436x^280+9900x^282+2680x^283+2300x^284+604x^285+11100x^287+2800x^288+3040x^289+1248x^290+11100x^292+2520x^293+2280x^294+516x^295+7940x^297+1900x^298+1700x^299+16x^300+2860x^302+480x^303+220x^304+28x^305+4x^310+16x^315+12x^320+12x^325+4x^330+4x^340

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 189 seconds.