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

generates a code of length 55 over Z7[X]/(X^2) who´s minimum homogenous weight is 321.

Homogenous weight enumerator: w(x)=1x^0+420x^321+768x^322+3444x^323+2100x^324+630x^328+600x^329+1344x^330+504x^331+1008x^335+972x^336+3444x^337+1512x^338+6x^343+42x^350+12x^357

The gray image is a linear code over GF(7) with n=385, k=5 and d=321.
This code was found by Heurico 1.16 in 3.62 seconds.