The generator matrix

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

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 1.16 in 0.0121 seconds.