The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  2 X^2+X+2 X^2  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+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 -6.48e-008 seconds.