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

generates a code of length 78 over Z5[X]/(X^2) who´s minimum homogenous weight is 302.

Homogenous weight enumerator: w(x)=1x^0+1320x^302+1440x^303+380x^304+8x^305+2140x^307+1620x^308+480x^309+40x^310+1860x^312+1140x^313+200x^314+64x^315+1280x^317+660x^318+280x^319+700x^322+780x^323+120x^324+700x^327+360x^328+40x^329+4x^330+8x^335

The gray image is a linear code over GF(5) with n=390, k=6 and d=302.
This code was found by Heurico 1.16 in 1.89 seconds.