The generator matrix

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

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+156x^285+140x^286+60x^288+364x^290+1760x^291+860x^293+496x^295+4160x^296+2360x^298+464x^300+7120x^301+4660x^303+316x^305+11240x^306+7360x^308+296x^310+13400x^311+7200x^313+208x^315+8880x^316+2500x^318+164x^320+3080x^321+168x^325+220x^326+148x^330+140x^335+88x^340+40x^345+52x^350+16x^355+8x^360

The gray image is a linear code over GF(5) with n=385, k=7 and d=285.
This code was found by Heurico 1.16 in 14.1 seconds.