The generator matrix
1 1 1 1 1 1 1 1 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+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+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 0 seconds.