The generator matrix

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

generates a code of length 77 over Z5[X]/(X^2) who´s minimum homogenous weight is 285.

Homogenous weight enumerator: w(x)=1x^0+164x^285+432x^290+400x^295+412x^300+340x^305+12500x^308+288x^310+316x^315+140x^320+168x^325+124x^330+136x^335+92x^340+60x^345+24x^350+16x^355+8x^360+4x^385

The gray image is a linear code over GF(5) with n=385, k=6 and d=285.
This code was found by Heurico 1.16 in 1.33 seconds.