The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^4+31x^6+128x^7+67x^8+1536x^9+67x^10+128x^11+31x^12+29x^14+1x^18

The gray image is a code over GF(2) with n=72, k=11 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.