The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2) 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 0.015 seconds.