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  X  1  1  1  1 3X  1  1
 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  1 4X+2 3X+4 X+2  4  1 X+1  4
 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  2 2X+2  1 2X 4X+4 3X+3  3 4X+3
 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 2X  0 2X 4X 3X 4X 4X 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+872x^280+1340x^281+500x^282+1100x^283+3740x^285+3800x^286+1260x^287+1800x^288+5800x^290+6200x^291+1460x^292+1800x^293+7016x^295+7360x^296+1700x^297+2000x^298+6152x^300+6020x^301+1340x^302+2100x^303+5388x^305+4040x^306+1080x^307+1000x^308+1584x^310+1240x^311+160x^312+200x^313+24x^315+12x^320+20x^325+8x^330+4x^335+4x^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 44.7 seconds.