The generator matrix

 1  1  1  1  X  2  X  X  1
 0  X  0 X^2+X+2 X^2+X  X X^2 X^2+X+2 X^2+2
 0  0 X^2+2 X^2  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 7.

Homogenous weight enumerator: w(x)=1x^0+48x^7+121x^8+196x^9+88x^10+40x^11+14x^12+4x^13

The gray image is a code over GF(2) with n=72, k=9 and d=28.
This code was found by Heurico 1.16 in -6.48e-008 seconds.