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

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+1100x^286+1420x^287+840x^288+40x^290+1640x^291+1600x^292+680x^293+48x^295+1580x^296+1040x^297+640x^298+1040x^301+920x^302+520x^303+620x^306+740x^307+320x^308+24x^310+520x^311+280x^312+8x^315+4x^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 30 seconds.