The generator matrix

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

generates a code of length 56 over Z7[X]/(X^2) who´s minimum homogenous weight is 328.

Homogenous weight enumerator: w(x)=1x^0+630x^328+5400x^329+1050x^330+504x^335+1860x^336+252x^337+924x^342+5412x^343+756x^344+18x^350

The gray image is a linear code over GF(7) with n=392, k=5 and d=328.
This code was found by Heurico 1.16 in 35.9 seconds.