The generator matrix

 1  0  1  1  1  2 X^2+X  1  X
 0  1 X+1 X^2+X+2 X^2+1  1  1  2  X
 0  0 X^2 X^2+2  2 X^2  0 X^2 X^2+2

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+72x^7+249x^8+404x^9+216x^10+64x^11+14x^12+4x^13

The gray image is a code over GF(2) with n=72, k=10 and d=28.
This code was found by Heurico 1.16 in 6.87e-008 seconds.