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

generates a code of length 49 over Z7[X]/(X^2) who´s minimum homogenous weight is 273.

Homogenous weight enumerator: w(x)=1x^0+402x^273+168x^274+42x^276+420x^278+1554x^279+4026x^280+1470x^281+756x^283+1680x^285+4158x^286+7494x^287+2814x^288+4536x^290+5670x^292+11718x^293+18306x^294+5754x^295+9072x^297+6636x^299+11382x^300+14802x^301+4200x^302+192x^308+138x^315+126x^322+108x^329+18x^336+6x^343

The gray image is a linear code over GF(7) with n=343, k=6 and d=273.
This code was found by Heurico 1.16 in 4.01 seconds.