The generator matrix

 1  1  1  1  X  1  1  X  X  2  2  X
 0 2X  0 2X 2X  0 2X  0 2X 2X  0  0

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

Homogenous weight enumerator: w(x)=1x^0+25x^12+6x^14

The gray image is a code over GF(2) with n=96, k=5 and d=48.
This code was found by Heurico 1.16 in 6.87e-008 seconds.