The generator matrix

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

generates a code of length 78 over Z5[X]/(X^2) who´s minimum homogenous weight is 300.

Homogenous weight enumerator: w(x)=1x^0+1028x^300+440x^302+640x^303+2552x^305+400x^307+420x^308+2144x^310+660x^312+400x^313+2316x^315+720x^317+880x^318+1588x^320+280x^322+160x^323+760x^325+160x^330+32x^335+16x^340+4x^345+12x^350+4x^355+4x^365+4x^370

The gray image is a linear code over GF(5) with n=390, k=6 and d=300.
This code was found by Heurico 1.16 in 1.78 seconds.