The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X 2X+2  X  X  X
 0  2  0 2X+2  0 2X  2  2  0 2X  0  0 2X+2 2X+2 2X  2  2
 0  0  2 2X+2  0 2X+2 2X+2 2X  0 2X+2 2X 2X+2 2X+2  2 2X  0  0
 0  0  0 2X  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  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+100x^14+285x^16+256x^17+312x^18+32x^20+36x^22+2x^24

The gray image is a code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 3.77 seconds.