The generator matrix

 1  1  1  1  X 2X  1  1 2X+2  1
 0  X  0 X+2 3X+2  X 2X+2 2X+2 2X  2
 0  0  2 2X+2 2X 2X+2 2X+2  2 2X+2  2

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+61x^8+108x^9+200x^10+72x^11+50x^12+12x^13+8x^14

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 -3.24e-008 seconds.