The generator matrix

 1  1  1  1  1  1  1  1  2
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2
 0  0  2  2  2  0  0  2  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+142x^8+96x^10+16x^12+1x^16

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.