The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+106x^6+256x^7+989x^8+1408x^9+968x^10+256x^11+106x^12+6x^14

The gray image is a code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 0.328 seconds.