The generator matrix

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

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+456x^8+592x^9+2032x^10+544x^11+452x^12+16x^13+3x^16

The gray image is a code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.16 in 163 seconds.