The generator matrix

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

generates a code of length 16 over Z7[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+252x^84+252x^86+588x^90+2646x^91+672x^93+3528x^97+7650x^98+1134x^100+42x^105+42x^112

The gray image is a linear code over GF(7) with n=112, k=5 and d=84.
This code was found by Heurico 1.16 in 0.0233 seconds.