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

generates a code of length 51 over Z7[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+84x^280+420x^285+336x^286+654x^287+42x^288+798x^290+840x^291+1008x^292+3024x^293+2436x^294+756x^295+3486x^297+1890x^298+2394x^299+5376x^300+3162x^301+4536x^302+11214x^304+6048x^305+4914x^306+11760x^307+6156x^308+9072x^309+13314x^311+5628x^312+5670x^313+8316x^314+3816x^315+126x^322+126x^329+138x^336+72x^343+36x^350

The gray image is a linear code over GF(7) with n=357, k=6 and d=280.
This code was found by Heurico 1.16 in 4.24 seconds.