The generator matrix

 1  1  1  1  1  1  1  0  1 2X 2X+2  1  1  1  1  X  1
 0  X  0  X 2X 3X  0  X  X 2X+2  X 2X+2 X+2 2X+2 X+2 X+2  0
 0  0  X  X 2X+2 3X+2 3X+2 2X 2X+2  X 3X 3X+2  0 2X+2  X 3X  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+34x^14+144x^15+175x^16+376x^17+133x^18+96x^19+24x^20+24x^21+16x^22+1x^26

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 seconds.