The generator matrix

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

generates a code of length 73 over Z7[X]/(X^2) who´s minimum homogenous weight is 427.

Homogenous weight enumerator: w(x)=1x^0+2544x^427+6954x^434+2490x^441+4770x^448+30x^455+12x^462+6x^483

The gray image is a linear code over GF(7) with n=511, k=5 and d=427.
This code was found by Heurico 1.16 in 0.176 seconds.