The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X X^2  X  X  X
 0 X^2+2  0 X^2  0  2 X^2+2 X^2+2  0  2  0  0 X^2 X^2  2 X^2+2 X^2+2
 0  0 X^2+2 X^2  0 X^2 X^2  2  0 X^2  2 X^2 X^2 X^2+2  2  0  0
 0  0  0  2  0  0  2  0  2  2  2  2  0  2  2  0  2
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  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+100x^14+285x^16+256x^17+312x^18+32x^20+36x^22+2x^24

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 3.73 seconds.