The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+168x^12+196x^14+119x^16+28x^18

The gray image is a code over GF(2) with n=56, k=9 and d=24.
This code was found by Heurico 1.13 in -9.54e-008 seconds.