The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X  0
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  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+15x^16+224x^17+15x^18+1x^34

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.