The generator matrix

 1  1  1  1  1  1  1  1  X  0  X  2  X  X  2  2  1
 0  X  2 X+2  0 X+2  2  X X+2  X  X  X  0  2  2  0  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+3x^16+16x^17+4x^18+8x^19

The gray image is a code over GF(2) with n=68, k=5 and d=32.
This code was found by Heurico 1.16 in 0.000903 seconds.