The generator matrix

 1  0  1  1  1  2  1 X+2  1  1  1  1  1  X
 0  1  1 X+2 X+1  1  2  1  3  2  2 X+2 X+3  1
 0  0  X  0  2 X+2  X  0  2 X+2  0  2  X  X
 0  0  0  2  2  0  2  2  0  0  2  2  0  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+166x^12+192x^14+143x^16+10x^20

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 0.00297 seconds.