The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  0  1  2  X  X  X
 0  X  0  X  2  0 X^2+X X^2+2 X^2+X X^2+2 X+2  X  X X^2  X X^2+X  2
 0  0  X  X X^2 X^2+X X^2+X X^2  0 X+2 X^2+X+2  2 X^2+X+2  X X^2 X^2+X X^2+X
 0  0  0  2  2  2  0  2  2  0  2  0  0  2  0  0  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+129x^14+272x^15+417x^16+458x^17+410x^18+190x^19+124x^20+38x^21+5x^22+2x^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.