The generator matrix

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

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+294x^12+384x^13+704x^14+384x^15+271x^16+10x^20

The gray image is a code over GF(2) with n=112, k=11 and d=48.
This code was found by Heurico 1.16 in 0.015 seconds.