The generator matrix

 1  1  1  1  X  X  X  1  1
 0  2  0  2  2  2  0  0  0
 0  0 2X  0  0  0 2X  0  0
 0  0  0 2X  0  0 2X  0  0
 0  0  0  0 2X  0 2X  0  0
 0  0  0  0  0 2X 2X  0  0

generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+23x^4+32x^6+32x^7+77x^8+704x^9+56x^10+32x^11+53x^12+8x^14+6x^16

The gray image is a code over GF(2) with n=72, k=10 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.