The generator matrix

 1  0  1  1 X^2+X  1  1  1  X  1  1 X^2+2 X+2  X X^2  1  1
 0  1  1 X^2+X  1 X+3 X^2+3 X^2  1  X X^2+X+3  1  1 X^2  X  2 X+3
 0  0  X  0  2 X^2 X^2+2  X  X X+2 X^2+X X^2+X+2 X^2+X+2  X  X  X X^2
 0  0  0  2  2  0  2  2  2  0  0  0  0  0  2  0  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+217x^14+412x^15+875x^16+1124x^17+870x^18+356x^19+200x^20+28x^21+9x^22+4x^24

The gray image is a code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 0.031 seconds.