The generator matrix

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

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+79x^8+96x^9+78x^10+2x^14

The gray image is a code over GF(2) with n=72, k=8 and d=32.
This code was found by Heurico 1.16 in 6.87e-008 seconds.