The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  1 X^2 X^2  1
 0 X^2+2  0  0  2 X^2+2 X^2+2 X^2  0 X^2  2  0 X^2  2 X^2+2  0 X^2+2
 0  0 X^2+2  0 X^2+2 X^2+2 X^2  2  0 X^2+2 X^2+2 X^2 X^2 X^2  2 X^2  0
 0  0  0 X^2+2 X^2  2 X^2 X^2  2  2  0  0 X^2+2 X^2+2  0 X^2+2 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+76x^14+56x^15+254x^16+272x^17+244x^18+56x^19+43x^20+16x^22+5x^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 0.203 seconds.