The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+42x^12+68x^13+312x^14+56x^15+13x^16+4x^17+15x^18+1x^26

The gray image is a code over GF(2) with n=112, k=9 and d=48.
This code was found by Heurico 1.16 in -3.24e-008 seconds.