The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+62x^14+76x^15+271x^16+40x^17+33x^18+12x^19+16x^20+1x^26

The gray image is a code over GF(2) with n=128, k=9 and d=56.
This code was found by Heurico 1.16 in 0.015 seconds.