The generator matrix

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

generates a code of length 14 over Z7[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+456x^70+360x^77+2058x^78+552x^84+12348x^85+780x^91+252x^98

The gray image is a linear code over GF(7) with n=98, k=5 and d=70.
This code was found by Heurico 1.16 in 1.58 seconds.