The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  0  1  X  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0  2 X^2+X+2 X^2+2 X^2+X  X X^2+2 X^2+X+2  0
 0  0 X^2+2  0 X^2 X^2  2 X^2  0 X^2 X^2  0  2  2 X^2 X^2+2  0
 0  0  0  2  2  0  2  2  2  2  0  0  0  2  0  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+64x^14+88x^15+168x^16+400x^17+152x^18+88x^19+51x^20+8x^22+3x^24+1x^28

The gray image is a code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 6.87e-008 seconds.