The generator matrix

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

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+6x^16+112x^17+7x^18+1x^24+1x^26

The gray image is a code over GF(2) with n=136, k=7 and d=64.
This code was found by Heurico 1.16 in 6.87e-008 seconds.