The generator matrix
1 1 1 1 X X X X 1
0 2 0 2 0 2 2 0 0
0 0 2 2 2 2 0 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+3x^8+54x^9+4x^10+2x^13
The gray image is a code over GF(2) with n=72, k=6 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.