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.