The generator matrix

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

generates a code of length 56 over Z7[X]/(X^2) who´s minimum homogenous weight is 322.

Homogenous weight enumerator: w(x)=1x^0+1848x^322+5922x^323+3150x^324+420x^327+8634x^329+16464x^330+6972x^331+630x^334+10422x^336+17514x^337+5712x^338+1008x^341+12360x^343+19782x^344+6804x^345+6x^357

The gray image is a linear code over GF(7) with n=392, k=6 and d=322.
This code was found by Heurico 1.16 in 3.93 seconds.