The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  X
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 X+2 2X  X 3X 3X+2 X+2  0
 0  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0
 0  0  0 2X  0  0 2X 2X  0 2X  0  0 2X  0  0 2X 2X
 0  0  0  0 2X 2X  0  0 2X 2X 2X  0 2X  0  0  0 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+73x^14+318x^16+256x^17+303x^18+63x^20+7x^22+1x^24+1x^26+1x^28

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 0.016 seconds.