The generator matrix

 1  0  1 X+2  1 2X+2  1 3X  1  0  1 X+2  1 2X+2  1 2X 3X
 0  1 X+2  1 2X+2  1 3X  1  0  1 X+2  1 2X+2  1 3X 2X  1
 0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X

generates a code of length 17 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+318x^16+128x^18+64x^20+1x^32

The gray image is a code over GF(2) with n=136, k=9 and d=64.
This code was found by Heurico 1.16 in 80.3 seconds.