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

generates a code of length 61 over Z7[X]/(X^2) who´s minimum homogenous weight is 355.

Homogenous weight enumerator: w(x)=1x^0+588x^355+126x^357+588x^358+4242x^359+1764x^362+84x^364+588x^365+1806x^366+588x^369+36x^371+882x^372+4242x^373+1176x^376+60x^378+24x^385+12x^392

The gray image is a linear code over GF(7) with n=427, k=5 and d=355.
This code was found by Heurico 1.16 in 0.291 seconds.