The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+118x^12+276x^14+112x^16+4x^18+1x^24

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 3.62e-008 seconds.