The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  0  1 2X+2  X  X  X
 0  X  0  X 2X  0 X+2 2X+2 X+2 2X+2 3X  X 2X+2  X 3X+2 2X 3X
 0  0  X  X  2 X+2 X+2  2  0 3X 3X+2 2X 3X+2 3X+2  2  X  X
 0  0  0 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X 2X

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

Homogenous weight enumerator: w(x)=1x^0+129x^14+272x^15+417x^16+458x^17+410x^18+190x^19+124x^20+38x^21+5x^22+2x^23+2x^24

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.