The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  2  0  2  0  2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2  0
 0  0 2X  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  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+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 -3.24e-008 seconds.