The generator matrix

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

generates a code of length 9 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+1x^8+24x^9+2x^10+4x^11

The gray image is a code over GF(2) with n=72, k=5 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.