The generator matrix
1 0 1 1 1 1 1 1 1 1 1 X
0 1 5X+1 3 5X+2 6 X 4X+1 X+3 4X+2 X+6 1
generates a code of length 12 over Z7[X]/(X^2) who´s minimum homogenous weight is 67.
Homogenous weight enumerator: w(x)=1x^0+504x^67+36x^70+588x^72+1260x^74+12x^84
The gray image is a linear code over GF(7) with n=84, k=4 and d=67.
This code was found by Heurico 1.16 in 0.00284 seconds.