The generator matrix

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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 304.

Homogenous weight enumerator: w(x)=1x^0+1280x^304+396x^305+2920x^309+704x^310+2380x^314+636x^315+2300x^319+908x^320+2720x^324+388x^325+860x^329+32x^330+40x^334+16x^335+8x^340+4x^345+8x^350+4x^355+12x^360+8x^365

The gray image is a linear code over GF(5) with n=395, k=6 and d=304.
This code was found by Heurico 1.16 in 78.2 seconds.