The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^14+7x^16

The gray image is a code over GF(2) with n=112, k=5 and d=56.
This code was found by Heurico 1.16 in -6.48e-008 seconds.