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

generates a code of length 63 over Z7[X]/(X^2) who´s minimum homogenous weight is 367.

Homogenous weight enumerator: w(x)=1x^0+840x^367+420x^369+3654x^371+2772x^374+630x^376+1284x^378+756x^381+1008x^383+3576x^385+1806x^388+54x^392+6x^406

The gray image is a linear code over GF(7) with n=441, k=5 and d=367.
This code was found by Heurico 1.16 in 80 seconds.