The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1  X  1  X  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  3 5X+2  6 5X+4  5  0 5X+1  3 5X+2  6 5X+4  5  1  5 5X+2 5X+1  6 X+5  1 5X+4  1  0  1  3  1  X 3X+5 X+5 X+3  X X+5 6X+5 5X+1 4X+4 X+3 4X+2 X+6 4X+1 4X+2  1 4X+2 6X+4 4X+3 2X+1  X 3X 6X+2 4X+4 X+2 X+4 3X+6  0
 0  0 5X  0 5X  X 5X  X 6X 2X  X 6X  0  0 6X 2X 3X 4X 3X 2X 4X  X  X 4X 2X  X 2X 6X 3X  X 5X  0 5X 3X  0  0 2X 2X 3X 6X 6X  X 4X  X  X 5X 2X 3X 6X 5X  X 3X 6X 3X  X
 0  0  0  X 4X 4X 3X 6X  0 6X  X 6X 5X 4X 3X 3X 6X 3X 5X 5X 5X 3X  0 4X 5X 5X 4X 4X 6X 5X 2X 2X  X 3X  X 4X  X 3X  X 4X 5X 3X  X  X 4X 3X 3X 4X 3X  X 6X 4X 4X  X  X

generates a code of length 55 over Z7[X]/(X^2) who´s minimum homogenous weight is 308.

Homogenous weight enumerator: w(x)=1x^0+246x^308+84x^309+546x^310+378x^314+2106x^315+2352x^316+4578x^317+1806x^321+4362x^322+4788x^323+7686x^324+5544x^328+12318x^329+11844x^330+18102x^331+6678x^335+11514x^336+9744x^337+12306x^338+204x^343+198x^350+102x^357+96x^364+54x^371+6x^378+6x^385

The gray image is a linear code over GF(7) with n=385, k=6 and d=308.
This code was found by Heurico 1.16 in 4.65 seconds.