The generator matrix

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

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+58x^6+104x^7+521x^8+688x^9+508x^10+104x^11+62x^12+2x^14

The gray image is a code over GF(2) with n=72, k=11 and d=24.
This code was found by Heurico 1.16 in 0.015 seconds.