The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+16x^9+28x^10+16x^11+2x^12+1x^16

The gray image is a code over GF(2) with n=80, k=6 and d=36.
This code was found by Heurico 1.16 in 3.62e-008 seconds.