The generator matrix

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

generates a code of length 17 over Z4[X]/(X^3+2,2X) 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 2.19 seconds.