The generator matrix

 1  1  1  1  1  X  1 2X+2  1
 0  X  0 3X+2 2X+2 3X+2 X+2 2X  0
 0  0  2  0 2X+2 2X 2X+2 2X+2  0
 0  0  0 2X 2X 2X 2X 2X 2X

generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+17x^6+84x^7+239x^8+352x^9+236x^10+68x^11+16x^12+8x^13+3x^14

The gray image is a code over GF(2) with n=72, k=10 and d=24.
This code was found by Heurico 1.16 in -3.24e-008 seconds.