The generator matrix

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

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+190x^16+64x^20+1x^32

The gray image is a code over GF(2) with n=68, k=8 and d=32.
This code was found by Heurico 1.16 in 59.6 seconds.