The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+20x^5+46x^6+64x^7+206x^8+1368x^9+220x^10+64x^11+32x^12+20x^13+6x^14+1x^16

The gray image is a code over GF(2) with n=72, k=11 and d=20.
This code was found by Heurico 1.16 in 6.87e-008 seconds.