The generator matrix

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

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+164x^14+64x^15+629x^16+384x^17+584x^18+64x^19+128x^20+20x^22+10x^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 11.8 seconds.