The generator matrix

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

generates a code of length 14 over Z7[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+228x^56+792x^63+1398x^70+2928x^77+14406x^78+4668x^84+86436x^85+4560x^91+2232x^98

The gray image is a linear code over GF(7) with n=98, k=6 and d=56.
This code was found by Heurico 1.16 in 1.64 seconds.