The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+100x^14+157x^16+184x^18+32x^20+36x^22+2x^24

The gray image is a code over GF(2) with n=68, k=9 and d=28.
This code was found by Heurico 1.16 in 1.51 seconds.