The generator matrix

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

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+88x^14+202x^15+489x^16+516x^17+484x^18+160x^19+84x^20+12x^21+4x^22+6x^23+2x^24

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.