The generator matrix

 1  1  1  1  1  1  1  1 X^2
 0 X^2+2  0 X^2+2  0  2 X^2+2 X^2  2
 0  0  2  0  0  2  2  2  0
 0  0  0  2  2  2  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+78x^8+128x^9+32x^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 3.62e-008 seconds.