The generator matrix

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

generates a code of length 74 over Z5[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+592x^280+1380x^281+1280x^282+480x^283+480x^284+2620x^285+4000x^286+2720x^287+800x^288+1100x^289+3504x^290+6100x^291+3620x^292+1200x^293+1080x^294+5140x^295+6960x^296+3840x^297+920x^298+960x^299+4172x^300+6020x^301+3260x^302+1040x^303+1040x^304+3432x^305+4400x^306+2200x^307+480x^308+340x^309+1088x^310+1140x^311+580x^312+80x^313+36x^315+8x^320+20x^325+4x^330+8x^340

The gray image is a linear code over GF(5) with n=370, k=7 and d=280.
This code was found by Heurico 1.16 in 20.7 seconds.