The generator matrix
1 0 1 1 1 3X+2 1 1 2 1 1 3X 1 1 1 1 1
0 1 X+1 3X+2 2X+3 1 2 X+3 1 3X 2X+1 1 2X X+2 2X+2 X 0
generates a code of length 17 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+79x^16+96x^17+78x^18+2x^26
The gray image is a code over GF(2) with n=136, k=8 and d=64.
This code was found by Heurico 1.16 in 6.87e-008 seconds.