The generator matrix

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

generates a code of length 61 over Z7[X]/(X^2) who´s minimum homogenous weight is 349.

Homogenous weight enumerator: w(x)=1x^0+1092x^349+186x^350+672x^351+1176x^352+1050x^353+1218x^354+5964x^355+4074x^356+1188x^357+3612x^358+4536x^359+4536x^360+2310x^361+10164x^362+5502x^363+1872x^364+4872x^365+5922x^366+4242x^367+2310x^368+8820x^369+4746x^370+3150x^371+7308x^372+6888x^373+4578x^374+2394x^375+7980x^376+5166x^377+54x^378+48x^385+18x^392

The gray image is a linear code over GF(7) with n=427, k=6 and d=349.
This code was found by Heurico 1.16 in 4.54 seconds.