The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1
 0  2  0 2X+2  0 2X  2  2  0 2X+2 2X+2 2X 2X  2 2X+2 2X 2X
 0  0  2 2X+2  0 2X+2 2X+2 2X 2X 2X+2 2X 2X 2X+2 2X  2 2X  0
 0  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X  0  0 2X  0

generates a code of length 17 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+8x^14+32x^15+62x^16+320x^17+48x^18+32x^19+8x^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 -3.24e-008 seconds.