The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1
 0  2  0  0  0  0  0  2  0  2  2  0  0  2  0  2  2
 0  0  2  0  0  0  2  2  0  2  0  0  2  2  2  2  0
 0  0  0  2  0  0  2  0  0  2  2  2  2  0  0  2  0
 0  0  0  0  2  0  2  0  2  2  0  2  0  2  0  2  2
 0  0  0  0  0  2  2  0  2  0  2  0  0  2  2  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+16x^14+62x^16+384x^17+32x^18+16x^22+1x^32

The gray image is a code over GF(2) with n=136, k=9 and d=56.
This code was found by Heurico 1.16 in 3.81e-009 seconds.