The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+78x^8+352x^10+80x^12+1x^16

The gray image is a code over GF(2) with n=80, k=9 and d=32.
This code was found by Heurico 1.16 in 6.87e-008 seconds.