The generator matrix

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

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+28x^14+78x^15+150x^16+62x^17+94x^18+26x^19+40x^20+26x^21+6x^22+1x^24

The gray image is a code over GF(2) with n=68, k=9 and d=28.
This code was found by Heurico 1.13 in -6.29e-008 seconds.