The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+7x^8+112x^9+7x^10+1x^18

The gray image is a code over GF(2) with n=72, k=7 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.