The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  2  2 X^2  1  1 X+2  1
 0  1  1 X^2 X+1  1  0 X^2+X+3  1 X+2  1  1  X  0 X^2+X+2  1  2
 0  0  X X+2  2 X+2 X^2+2 X^2+X+2 X^2+2  0 X^2 X+2  X X^2+X+2 X^2+X X^2+X  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+54x^14+264x^15+335x^16+796x^17+317x^18+180x^19+56x^20+36x^21+4x^22+4x^23+1x^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 0.015 seconds.