The generator matrix

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

generates a code of length 47 over Z7[X]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+2520x^268+4074x^269+84x^270+252x^271+1008x^272+2646x^273+1218x^274+10164x^275+12138x^276+1008x^277+1260x^278+2688x^279+3900x^280+1092x^281+13272x^282+12894x^283+3024x^284+2604x^285+4536x^286+6060x^287+1806x^288+15204x^289+14112x^290+36x^294+24x^301+12x^308+12x^315

The gray image is a linear code over GF(7) with n=329, k=6 and d=268.
This code was found by Heurico 1.16 in 3.47 seconds.