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

generates a code of length 56 over Z7[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+420x^315+420x^316+546x^317+3150x^321+1488x^322+2688x^323+1386x^324+8190x^328+3024x^329+5880x^330+3150x^331+23562x^335+6072x^336+11424x^337+5880x^338+22722x^342+5178x^343+8400x^344+3444x^345+222x^350+150x^357+126x^364+48x^371+54x^378+24x^385

The gray image is a linear code over GF(7) with n=392, k=6 and d=315.
This code was found by Heurico 1.16 in 4.6 seconds.