The generator matrix

 1  1  1  1  1  1  1  0  1  2 X^2+2  1  1  1  1  X  1
 0  X  0  X  2 X+2  0  X  X X^2  X X^2+2 X^2+X+2 X^2+2 X^2+X+2 X^2  2
 0  0  X  X X^2 X^2+X X^2+X  2 X^2  X X^2+X  X  0 X^2 X^2+X  X  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+22x^14+142x^15+181x^16+390x^17+147x^18+74x^19+26x^20+34x^21+6x^22+1x^26

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.