The generator matrix

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

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+198x^12+128x^13+384x^14+128x^15+175x^16+10x^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 3.97 seconds.