The generator matrix

 1  1  1  1  1  X  X  X  1  1
 0 2X  0 2X  0  0 2X 2X  0 2X
 0  0 2X 2X  0 2X 2X  0 2X 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+6x^9+51x^10+3x^12+2x^13+1x^14

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.