The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+132x^14+192x^15+457x^16+512x^17+442x^18+192x^19+96x^20+16x^22+6x^24+2x^26

The gray image is a code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 2.2 seconds.