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

generates a code of length 74 over Z5[X]/(X^2) who´s minimum homogenous weight is 286.

Homogenous weight enumerator: w(x)=1x^0+1080x^286+1460x^287+840x^288+48x^290+1540x^291+1520x^292+760x^293+40x^295+1720x^296+1180x^297+520x^298+960x^301+880x^302+520x^303+860x^306+520x^307+360x^308+24x^310+340x^311+440x^312+12x^320

The gray image is a linear code over GF(5) with n=370, k=6 and d=286.
This code was found by Heurico 1.16 in 2.94 seconds.