The generator matrix

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

generates a code of length 15 over Z7[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+180x^84+2058x^90+90x^91+72x^105

The gray image is a linear code over GF(7) with n=105, k=4 and d=84.
This code was found by Heurico 1.16 in 0.00807 seconds.