The generator matrix

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

generates a code of length 14 over Z7[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+162x^77+294x^78+60x^84+1764x^85+66x^91+54x^98

The gray image is a linear code over GF(7) with n=98, k=4 and d=77.
This code was found by Heurico 1.16 in 0.00142 seconds.