The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+16x^13+28x^14+16x^15+1x^16+2x^20

The gray image is a code over GF(2) with n=112, k=6 and d=52.
This code was found by Heurico 1.16 in 1.05e-007 seconds.