The generator matrix

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

generates a code of length 14 over Z7[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+588x^79+336x^84+1470x^86+6x^98

The gray image is a linear code over GF(7) with n=98, k=4 and d=79.
This code was found by Heurico 1.16 in 0.000708 seconds.