The generator matrix

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

generates a code of length 16 over Z7[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+264x^70+1074x^77+1842x^84+14406x^90+3492x^91+86436x^97+4812x^98+3978x^105+1344x^112

The gray image is a linear code over GF(7) with n=112, k=6 and d=70.
This code was found by Heurico 1.16 in 2.21 seconds.