The generator matrix

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

generates a code of length 72 over Z5[X]/(X^2) who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+1540x^278+1080x^279+100x^280+2900x^283+1360x^284+308x^285+2020x^288+920x^289+60x^290+1700x^293+960x^294+40x^295+1240x^298+480x^299+84x^300+600x^303+200x^304+20x^305+12x^310

The gray image is a linear code over GF(5) with n=360, k=6 and d=278.
This code was found by Heurico 1.16 in 3.05 seconds.