The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1 2X 2X  1 3X 2X+2  1  1
 0  1  1 2X+2 X+1  1  0 X+3  1 3X  1  1 3X+2  1  X  0 2X
 0  0  X 3X 2X 3X  2 X+2  2  0 2X+2 3X 3X+2 X+2 3X X+2  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+54x^14+248x^15+407x^16+692x^17+365x^18+180x^19+64x^20+28x^21+4x^22+4x^23+1x^26

The gray image is a code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 0.016 seconds.