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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+1220x^306+1420x^307+840x^308+16x^310+1740x^311+1580x^312+760x^313+44x^315+1160x^316+1100x^317+680x^318+52x^320+1100x^321+960x^322+320x^323+760x^326+560x^327+280x^328+520x^331+380x^332+120x^333+8x^335+4x^340

The gray image is a linear code over GF(5) with n=395, k=6 and d=306.
This code was found by Heurico 1.16 in 14.2 seconds.