The generator matrix
1 1
0 5X+1
generates a code of length 2 over Z7[X]/(X^2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+84x^6+12x^7+1764x^12+504x^13+36x^14
The gray image is a linear code over GF(7) with n=14, k=4 and d=6.
This code was found by Heurico 1.16 in 3.19e-005 seconds.