The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+26x^6+292x^7+785x^8+1916x^9+748x^10+284x^11+38x^12+4x^13+2x^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 0.016 seconds.