The generator matrix

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

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+42x^6+174x^7+347x^8+942x^9+326x^10+154x^11+52x^12+10x^13

The gray image is a code over GF(2) with n=72, k=11 and d=24.
This code was found by Heurico 1.16 in -1.16e-007 seconds.