The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+15x^16+96x^17+15x^18+1x^34

The gray image is a code over GF(2) with n=68, k=7 and d=32.
This code was found by Heurico 1.16 in 0.00132 seconds.