The generator matrix

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

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+108x^12+280x^13+300x^14+208x^15+95x^16+24x^17+4x^18+4x^20

The gray image is a code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in -8.01e-008 seconds.