The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  X 3X 3X  0  X 3X 2X 2X 2X  0  X 3X 2X
 0  0  X 5X 3X 2X 4X 2X  X 5X  X 4X 5X 4X  0 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+54x^84+114x^91+2058x^96+96x^98+18x^105+60x^112

The gray image is a linear code over GF(7) with n=112, k=4 and d=84.
This code was found by Heurico 1.16 in 0.00176 seconds.