The generator matrix
1 1 1 1 1 1 1 1 X 0 X X^2+2 X 2 X X^2 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 X^2+X X X+2 X X^2+X+2 X X X 0
generates a code of length 17 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+6x^16+112x^17+7x^18+1x^24+1x^26
The gray image is a code over GF(2) with n=136, k=7 and d=64.
This code was found by Heurico 1.16 in 1.05e-007 seconds.